ScorpTech x402 API

Build EVM calldata offline: function selector + ABI-encoded arguments from a human signature such as transfer(address,uint256) or exactInputSingle((address,address,uint24,address,uint256,uint256,uint160)). Tuples/structs, fixed and dynamic arrays, bytes, strings and signed ints supported. mode=params gives abi.encode without a selector, mode=packed gives abi.encodePacked plus its keccak256 (as used for hashes and signatures). Returns hex, 32-byte words and length. Price: $0.003 USDC per successful call (x402, Solana). Same tool over HTTPS: GET https://scorptech.it.com/api/x402/v1/abi-encode

sigma(n) minus 2n. A perfect number gives 0, an abundant number gives a positive value, and a deficient number gives a negative value. 12 gives 4, 6 gives 0, 10 gives -2, and 1 gives -1. n runs from 1 to 10000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/abundance

The abundancy sigma(n)/n as a reduced fraction. 1 is 1/1, 4 is 7/4, 6 is 2/1, and 12 is 7/3. n runs from 1 to 1000000000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/abundancy

Whether n is an Achilles number: powerful, but not a perfect power. 72 and 108 are Achilles. 36 is a square, and 1 is a perfect power, so neither is Achilles. n runs from 1 to 1000000000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/achilles

Additive persistence: how many times the decimal digits of n must be summed to reach a single digit, and that digit. 199 takes 3 steps and ends at 1. A single digit takes 0 steps. n runs from 0 to 999999999999999. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/additive-persistence

US airport delay status from the FAA NAS Status feed (ground delay programs, ground stops, closures, arrival/departure delays) plus OurAirports metadata (name, city, ICAO/IATA, lat/lon). Pass ?airport=SFO (IATA) or KSFO (ICAO), or omit for a nationwide overview. Public-domain sources. Price: $0.01 USDC per successful call (x402, Solana). Same tool over HTTPS: GET https://scorptech.it.com/api/x402/v1/airport-status

The aliquot part of n, the sum of proper divisors. The aliquot part of 1 is 0, of 9 is 4, and of 6 is 6. n runs from 1 to 1000000000000. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/aliquot

Whether sigma(n) = 2*n - 1. Powers of two, including 1, are almost perfect. 16 gives sigma 31. 6 and 10 are not. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/almost-perfect

The alternating factorial af(n) = n! - (n-1)! + (n-2)! - ... ending at 1. af(1) is 1, af(3) is 5, and af(4) is 19. n runs from 1 to 200. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/alt-factorial

The sum of alternating factorials from lo through hi inclusive. The sum from af(1) through af(5) is 127. lo must not pass hi. Each index runs from 1 to 200. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/alt-sum

The alternating factorial a(n) = n! - a(n-1), with a(1) = 1. a(3) is 5, a(4) is 19, a(5) is 101, a(6) is 619, and a(8) is 35899. n runs from 1 to 18. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/alternating-factorial

The alternating factorial a(n) modulo m. a(5) mod 10 is 1, a(6) mod 100 is 19, and a(4) mod 5 is 4. n runs from 1 to 18 and m runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/alternating-mod

The smallest m at least n, and at most 12, whose alternating factorial is prime. 1 gives 3, 3 stays 3, and 9 gives 10. If none remains through 12, the input is rejected. n runs from 1 to 12. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/alternating-next

Whether the alternating factorial a(n) is prime. It is for 3, 4, 5, 6, 7, 8, and 10. It is not for 1, 2, 9, or 12. n runs from 1 to 12. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/alternating-prime

The sum of the alternating factorials from 1 through n. Through 1 it is 1, through 3 it is 7, through 5 it is 127, through 6 it is 746, and through 8 it is 41066. n runs from 1 to 18. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/alternating-sum

Whether n is amicable, and its partner when it is. The partner of 220 is 284, and the partner of 284 is 220. A perfect number such as 6 is not amicable, and then the partner is 0. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/amicable

The Apery number A(n), the sum of C(n,k)^2 * C(n+k,k)^2 for k from 0 to n. A(0) is 1, A(1) is 5, A(2) is 73, A(3) is 1445, and A(5) is 819005. n runs from 0 to 11. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/apery

A(n) modulo m. A(1) mod 2 is 1, A(5) mod 10 is 5, and A(8) mod 1000 is 425. n runs from 0 to 11 and m runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/apery-mod

Whether the Apery number A(n) is prime. A(1) and A(2) are prime. A(0), A(3), A(5), and A(8) are not. n runs from 0 to 11. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/apery-prime

The sum of the Apery numbers A(0) through A(n). Through 0 it is 1, through 2 it is 79, and through 5 it is 853530. n runs from 0 to 11. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/apery-sum

One summand of the Apery number, C(n,k)^2 * C(n+k,k)^2. The k=1 summand of A(2) is 36 and the k=0 summand is 1. A k past n is 0. n and k run from 0 to 11. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/apery-term

How many arithmetic numbers are at most n. Through 1 there is 1, through 2 there is 1, through 6 there are 4, through 15 there are 9, and through 20 there are 12. n runs from 1 to 5000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/arithmetic-count

The arithmetic derivative of n. 0 and 1 give 0, a prime gives 1, 4 gives 4, 6 gives 5, 8 gives 12, and 12 gives 16. n runs from 0 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/arithmetic-derivative

The average of the divisors of n, when that average is an integer. 1 gives 1, 3 gives 2, 6 gives 3, 7 gives 4, 15 gives 6, and 20 gives 7. A non-integer average is rejected. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/arithmetic-mean

The smallest arithmetic number that is at least n. 1 stays 1, 2 gives 3, 4 gives 5, 8 gives 11, and 13 stays 13. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/arithmetic-next

Whether the average of the divisors of n is an integer. 1, 3, 6, 15, and 20 are. 2, 4, 8, and 12 are not. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/arithmetic-number

The second arithmetic derivative of n. 6 goes 5 then 1. 8 goes 12 then 16. 4 stays 4. 0 and 1 stay 0. n runs from 0 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/arithmetic-second

The sum of the arithmetic numbers that are at most n. Through 1 it is 1, through 6 it is 15, through 15 it is 75, and through 20 it is 131. n runs from 1 to 5000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/arithmetic-sum

Search arXiv papers: title, authors, full abstract, categories, dates, DOI/journal ref and direct abs + PDF links. Plain keywords or arXiv field syntax (ti:, au:, abs:, cat:, AND/OR), optional category filter and sort by relevance or date. Price: $0.01 USDC per successful call (x402, Solana). Same tool over HTTPS: GET https://scorptech.it.com/api/x402/v1/arxiv-search

Whether n^2 ends with n. 1, 5, 6, 25, 76, 376, 625, and 9376 do. 10 does not. n runs from 1 to 10000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/automorphic

Whether n is prime and equal to the average of the previous prime and the next prime. 5, 53, 157, and 1103 are. 2, 3, 7, and 11 are not. n runs from 1 to 5000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/balanced-prime

The balanced ternary digits of n. -1 is written as T. 0 is "0", 2 is "1T", 4 is "11", 5 is "1TT", and 6 is "1T0". n runs from 0 to 999999999999999. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/balanced-ternary

The ballot number B(n, k) = (n-k+1)/(n+1) * binom(n+k, k), for 0 <= k <= n. B(n, n) is the nth Catalan number. k above n is rejected. Both indexes run up to 2048. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/ballot

Validate bank routing identifiers offline (IBAN is covered by /v1/iban-validate): US ABA routing numbers (3-7-1 checksum, Federal Reserve district, thrift / electronic ranges), SWIFT / BIC (bank, ISO country, location, branch, test and passive BICs), Mexican CLABE (checksum, bank, plaza), Argentine CBU (both check digits), Canadian routing numbers (EFT 0YYYXXXXX and MICR XXXXX-YYY, institution names), UK sort codes, Australian BSB (bank and state) and Indian IFSC (bank). Auto-detects the type from the format. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: GET https://scorptech.it.com/api/x402/v1/bank-id-validate

Generate a 1D barcode as SVG (plus base64 data URI and the raw module pattern): Code 128 (any ASCII, automatic A / B / C subset switching for the shortest symbol), GS1-128 shipping / logistics labels from "(01)…(17)…(10)…" application identifiers (FNC1 separators, SSCC / GTIN check digits verified), EAN-13, EAN-8, UPC-A and ITF-14 (check digit computed when omitted, verified when given) and Code 39 (optional mod-43 check). Options: module width, bar height, quiet zone, human-readable text, colours. For product labels, shipping cartons, inventory and tickets. Price: $0.002 USDC per successful call (x402, Solana). Same tool over HTTPS: GET https://scorptech.it.com/api/x402/v1/barcode-generate

Convert an integer from one base to another. Bases run from 2 to 36, and letters may be any case. A digit that is not valid in the source base is rejected. The result is the digit string in the target base. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/base-convert

The Baum-Sweet bit of n. It is 1 when every run of 0s in the binary expansion has even length, and 0 when some run of 0s has odd length. b(0) is 1 and b(2) is 0. n runs from 0 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/baum-sweet

The Beatty term floor(n*sqrt(d)). floor(5*sqrt(2)) is 7, and floor(2*sqrt(3)) is 3. n runs from 0 to 1000000 and d runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/beatty

floor(n*sqrt(2)). n=1 gives 1, n=2 gives 2, n=3 gives 4, n=5 gives 7, and n=10 gives 14. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/beatty-sqrt2

The Beatty complement of sqrt(2), floor(n*(2+sqrt(2))). n=1 gives 3, n=2 gives 6, n=3 gives 10, and n=5 gives 17. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/beatty-sqrt2-comp

The nth Bell number, the number of partitions of a set of n objects. B(0) and B(1) are 1, and B(5) is 52. n runs from 0 to 80. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/bell

The sum of Bell numbers from lo through hi inclusive. lo must not pass hi. Each index runs from 0 to 80. Past 15 digits the sum is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/bell-sum

The nth Bernoulli number as a reduced fraction, from the Akiyama-Tanigawa algorithm. B0 is 1, B1 is 1/2, B2 is 1/6, and B4 is -1/30. Odd indices after 1 are 0. n runs from 0 to 40. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/bernoulli

The von Staudt denominator of B(m) for even m at least 2: the product of primes p such that p-1 divides m. The denominator of B2 is 6, and of B4 is 30. An odd m is rejected. m runs from 2 to 40. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/bernoulli-denom

The sum of Bernoulli numbers B0 through Bn, as a reduced fraction. The sum through B1 is 3/2, and through B2 is 5/3. n runs from 0 to 40. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/bernoulli-sum

Whether n and m are betrothed: the sum of proper divisors of n is m+1, and the sum for m is n+1, with m different from n. 48 pairs with 75, and 140 pairs with 195. The partner is 0 when n is not betrothed. n runs from 1 to 100000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/betrothed

Point on a cubic Bezier at t, as an exact fraction. t is between 0 and 1. The arch (0,0), (0,1), (1,1), (1,0) at one half is (1/2, 3/4). Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/bezier-cubic

Control points of the derivative of a quadratic or cubic Bezier. A cubic derivative is a quadratic, and each control is the degree times the step to the next point. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/bezier-derivative

Point on a quadratic Bezier at t, as an exact fraction. (0,0), (1,1), (2,0) at one half is (1, 1/2). Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/bezier-quadratic

Split a quadratic or cubic Bezier at t by de Casteljau. Left and right are the two new control polygons, and they meet at the point on the curve. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/bezier-split

Tangent vector of a quadratic or cubic Bezier at t. It is the derivative curve evaluated at t. The arch (0,0), (0,1), (1,1), (1,0) at one half has tangent (3/2, 0). Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/bezier-tangent

The number of prime factors of n counted with multiplicity. Omega(1) is 0, Omega(4) is 2, and Omega(12) is 3. n runs from 1 to 1000000000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/big-omega

The number of binary partitions of n, partitions into powers of two. b(0) is 1. Odd n copies b(n-1). Even n is b(n-1) plus b(n/2). b(1) is 1, b(4) is 4, and b(10) is 14. n runs from 0 to 1000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/binary-partition

The sum of the binary partition numbers from b(0) through b(n). Through 0 it is 1, through 4 it is 10, through 10 it is 60, and through 20 it is 390. n runs from 0 to 1000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/binary-partition-sum

The binomial coefficient C(n, k). k must not exceed n, and both indexes run up to 4096. An optional modulus reduces the coefficient; zero is rejected. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/binom

The bit length of n: 0 for 0, and one more than the position of the highest 1 bit otherwise. 1 has length 1, 255 has length 8, and 256 has length 9. n runs from 0 to 999999999999999. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/bit-length

Reverse the lowest width bits of n. 13 reversed in width 4 is 11. 1 reversed in width 8 is 128. n must be smaller than 2^width. width runs from 1 to 62, and n runs from 0 to 999999999999999. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/bit-reverse

Whether every 1 bit of a is also a 1 bit of b. 3 is a bit-subset of 7. 3 is not a bit-subset of 5. 0 is a bit-subset of 0. Both run from 0 to 999999999999999. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/bit-subset

Whether the bi-unitary divisors of n sum to more than 2n. 24 and 48 do. 6, 16, and 36 do not. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/biunitary-abundant

How many bi-unitary divisors n has. 1 has 1, 4 and 9 have 2, 8 has 4, and 16 has 4. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/biunitary-count

Whether the bi-unitary divisors of n sum to less than 2n. 1, 16, and 36 do. 6, 24, and 48 do not. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/biunitary-deficient

Whether the bi-unitary divisors of n sum to 2n. 6, 60, and 90 do. 16, 24, 36, and 48 do not. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/biunitary-perfect

The sum of the bi-unitary divisors of n. For a prime power p^e the exponents run from 0 through e, skipping the middle one when e is even. 6 gives 12, 16 gives 27, 36 gives 50, and 48 gives 108. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/biunitary-sigma

European option pricing (Black-Scholes-Merton with continuous dividend yield): call and put prices, delta, gamma, vega, theta per day, rho, d1/d2 and probability of finishing in the money; with a market price it solves implied volatility. Works for equity, index and crypto options (set the yield to 0). Price: $0.002 USDC per successful call (x402, Solana). Same tool over HTTPS: GET https://scorptech.it.com/api/x402/v1/black-scholes

Any BLS time series by id (CPI, payrolls, unemployment, state/metro LAUS, PPI, JOLTS, ECI ...) for a year range: observations newest first with preliminary flags and footnotes, latest value, MoM / YoY change. Up to 25 series per call. Includes BLS retrieval date and disclaimer. Price: $0.01 USDC per successful call (x402, Solana). Same tool over HTTPS: GET https://scorptech.it.com/api/x402/v1/bls-series

Whether n is a product of two distinct primes that are both 3 mod 4. 21, 33, and 77 are. 9, 15, 25, 35, and 49 are not. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/blum

How many Blum integers are at most n. Through 20 there are 0, through 21 there is 1, through 33 there are 2, and through 100 there are 6. n runs from 1 to 5000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/blum-count

The two prime factors of a Blum integer, smaller first. 21 gives 3,7. 33 gives 3,11. 77 gives 7,11. A non-Blum integer is rejected. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/blum-factors

The smallest Blum integer that is at least n. 1 gives 21, 22 gives 33, 34 gives 57, and 78 gives 93. n runs from 1 to 10000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/blum-next

The sum of the Blum integers that are at most n. Through 21 it is 21, through 33 it is 54, through 77 it is 257, and through 100 it is 350. n runs from 1 to 5000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/blum-sum

Fixed-coupon bond math: price from yield or yield to maturity from price (clean and dirty, with accrued interest for fractional periods), current yield, Macaulay and modified duration, convexity and DV01, plus the cash-flow schedule. Treasury, corporate or zero-coupon bonds; any coupon frequency. Price: $0.002 USDC per successful call (x402, Solana). Same tool over HTTPS: GET https://scorptech.it.com/api/x402/v1/bond-calc

Whether n! + 1 is a perfect square. 4! + 1 = 5^2, 5! + 1 = 11^2, and 7! + 1 = 71^2. The root is 0 when it is not a square. n runs from 1 to 12. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/brocard

The two historic Unix sums, matching GNU sum. bsd rotates the 16-bit sum right and counts 1024-byte blocks. sysv reduces modulo 65535, keeps 65535 when the total is a positive multiple of it, and counts 512-byte blocks. "123456789" is bsd 53615 and sysv 477. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/byte-sum

The cake number, the most pieces of space cut by n planes: (n^3 + 5*n + 6)/6. Zero planes give 1, three give 8, and five give 26. n runs from 0 to 100000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/cake-number

The Calkin-Wilf tree. Give n to get the nth positive rational, starting at 1/1, or give a reduced num and den to get its index. The two answers must agree when both are sent. An unreduced fraction is rejected. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/calkin-wilf

The Cantor bit of n. It is 1 when every base-3 digit of n is 0 or 1, and 0 when a digit is 2. Bit 0 is 1, bit 2 is 0, and bit 4 is 1. n runs from 0 to 999999999999999. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/cantor-bit

How many integers from 0 through n have only the digits 0 and 1 in base 3. The count through 0 is 1, through 2 is 2, and through 8 is 4. n runs from 0 to 999999999999999. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/cantor-count

Payment card number checks without storing anything: Luhn checksum, brand / network from the IIN (Visa, Mastercard incl. 2-series, Amex, Discover, Diners, JCB, UnionPay, Maestro, Mir, Elo, Hipercard, Verve, RuPay, Dankort, Troy, UATP), allowed lengths, CVV length, card-number spacing, known public test numbers (Stripe, Braintree, Adyen) and expiry validity. Returns only the PCI-safe first 6 / last 4 — never the full number. Up to 100 numbers per call. POST so numbers stay out of URLs and logs. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/card-validate

Carmichael's lambda of n, the exponent of the multiplicative group mod n. lambda(1) is 1, lambda(8) is 2, lambda(p) is p-1, and lambda(15) is 4. n runs from 1 to 1000000000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/carmichael

How many Carmichael numbers are at most n. Through 560 there are 0, through 561 there is 1, through 1729 there are 3, and through 10000 there are 7. n runs from 1 to 10000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/carmichael-count

The prime factors of a Carmichael number, ascending and comma-separated. 561 gives 3,11,17. 1105 gives 5,13,17. 1729 gives 7,13,19. A non-Carmichael number is rejected. n runs from 1 to 20000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/carmichael-factors

The smallest Carmichael number that is at least n. 1 gives 561, 562 gives 1105, 2000 gives 2465, and 2822 gives 6601. n runs from 1 to 10000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/carmichael-next

Whether n is a Carmichael number: composite, squarefree, and p-1 divides n-1 for every prime p dividing n. 561, 1105, and 1729 are. 1, 91, and 341 are not. n runs from 1 to 20000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/carmichael-number

The sum of the Carmichael numbers that are at most n. Through 561 it is 561, through 1105 it is 1666, through 1729 it is 3395, and through 8911 it is 24193. n runs from 1 to 10000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/carmichael-sum

The nth Carol number, (2^n - 1)^2 - 2. n=1 gives -1, n=2 gives 7, and n=3 gives 47. n runs from 1 to 128. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/carol

CAS Registry Number check digit. Two to seven digits, a hyphen, two digits, a hyphen and a check digit. No leading zero. From the right, digits are weighted 1, 2, 3 and the total mod 10 is the check. A number typed without hyphens is split the same way. This does not look the substance up. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: GET https://scorptech.it.com/api/x402/v1/cas-validate

The nth Catalan number. C0 and C1 are 1, C2 is 2, C3 is 5, and C_n = binom(2n, n) / (n+1). n runs from 0 to 2048. An optional modulus reduces the term; zero is rejected. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/catalan

The number of trees on n labeled vertices, n^(n-2). One vertex gives 1, two give 1, three give 3, and four give 16. n runs from 1 to 30. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/cayley

The number of rooted trees on n labeled vertices, n^(n-1). Four vertices give 64. n runs from 1 to 30. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/cayley-rooted

US Census Bureau geocoder: a one-line US street address (or a lat/lon) to matched address and coordinates plus Census geographies: state and county with FIPS codes, census tract, block group and block GEOID, place/city, congressional district, state legislative districts, ZCTA, metro/micro area and urban area where available. Public-domain US government data; useful for district lookups, data joins and address normalisation. Price: $0.01 USDC per successful call (x402, Solana). Same tool over HTTPS: GET https://scorptech.it.com/api/x402/v1/census-geographies

The nth centered s-gonal number, s*n*(n-1)/2 + 1. Centered triangular 4 is 19, centered square 2 is 5, and centered hexagonal 3 is 19. s runs from 3 to 20 and n from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/centered-polygonal

The nth central binomial coefficient (2n)!/(n!)^2. C(0) is 1, C(1) is 2, C(5) is 252, and C(10) is 184756. n runs from 0 to 200. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/central-binomial

The index n with central binomial coefficient C(n) equal to value. 1 is index 0, and 2 is index 1. A number that is not a term, or a leading zero, is rejected. value is a decimal integer of at most 600 digits. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/central-index

C(n) mod m for the central binomial coefficients. C(10) mod 7 is 5. The modulus is a positive decimal integer, and zero is rejected. n runs from 0 to 200. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/central-mod

The ratio C(n)/C(n-1) = (4n-2)/n in lowest terms. For 1 it is 2/1, for 2 it is 3/1, and for 3 it is 10/3. n runs from 1 to 200. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/central-ratio

The sum of central binomial coefficients from lo through hi. The sum from C(0) through C(5) is 351. lo must not pass hi. Each index runs from 0 to 200. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/central-sum

Best rational approximation with a denominator up to maxDen. It searches the convergents and the intermediate fractions. 355/113 with maxDen 7 is 22/7. With maxDen 100 it is 311/99. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/cf-best

One convergent of a continued fraction. Index 0 is a0/1. The last index is the value itself. 13/8 at index 3 is 5/3. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/cf-convergent

Continued fraction of a non-negative rational, by the Euclidean algorithm. 13/8 is [1; 1, 1, 1, 2]. 355/113 is [3; 7, 16]. A trailing 1 is folded into the previous term, so this is the short form. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/cf-expand

Continued fraction of a square root. sqrt(2) is [1; 2, 2, 2, ...] and the period is 1. sqrt(3) has period 2. A perfect square is one term and period 0. The period is the repeating length, even when fewer terms are requested. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: GET https://scorptech.it.com/api/x402/v1/cf-sqrt