{"openapi":"3.1.0","info":{"title":"Number Sequences API","version":"1.0.0","description":"Generate famous integer sequences and test membership, with exact big-integer maths. The generate endpoint returns the first N terms of a sequence — Fibonacci, Lucas, prime numbers, triangular, square, cube, factorial, Catalan, pentagonal and tetrahedral numbers, plus parameterised arithmetic (a start and a step), geometric (a start and a ratio) and powers (any base). The contains endpoint tells you whether a given number belongs to a sequence — is 233 a Fibonacci number, is 21 triangular, is 97 prime, is 720 a factorial — using fast closed-form tests for primes, squares, cubes, triangular, pentagonal and Fibonacci numbers and an exact search for the rest, and it returns the term index where it is known. Because everything is computed with arbitrary-precision integers, terms beyond the usual floating-point limit are returned exactly as decimal strings and never overflow. It runs entirely locally, so it is instant, deterministic and private. Ideal for education and maths tooling, coding challenges and puzzles, test-data generation, recreational mathematics and number-theory experiments. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This generates and tests integer sequences; to factorize a single number or get its divisors use a number-theory API.","contact":{"name":"PremiumApi","url":"https://www.oanor.com/by/premiumapi"}},"servers":[{"url":"https://api.oanor.com/sequences-api","description":"oanor gateway"}],"tags":[{"name":"Sequences"},{"name":"Meta"}],"components":{"securitySchemes":{"oanorKey":{"type":"apiKey","in":"header","name":"x-oanor-key","description":"Get your key at https://www.oanor.com/developer/keys"}}},"security":[{"oanorKey":[]}],"paths":{"/v1/contains":{"get":{"operationId":"get_v1_contains","tags":["Sequences"],"summary":"Test membership","description":"","parameters":[{"name":"sequence","in":"query","required":true,"description":"The sequence name","schema":{"type":"string"},"example":"fibonacci"},{"name":"value","in":"query","required":true,"description":"The integer to test","schema":{"type":"string"},"example":"233"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"value":"233","contains":true,"sequence":"fibonacci"},"meta":{"timestamp":"2026-06-03T09:25:02.621Z","request_id":"b01c8eb1-72f1-41c6-953a-27fa4ec2e9fe"},"status":"ok","message":"Test membership","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/generate":{"get":{"operationId":"get_v1_generate","tags":["Sequences"],"summary":"Generate a sequence","description":"","parameters":[{"name":"sequence","in":"query","required":true,"description":"fibonacci, lucas, primes, triangular, square, cube, factorial, catalan, pentagonal, tetrahedral, arithmetic, geometric, powers","schema":{"type":"string"},"example":"fibonacci"},{"name":"count","in":"query","required":false,"description":"How many terms (default 10, max 1000)","schema":{"type":"string"},"example":"10"},{"name":"start","in":"query","required":false,"description":"arithmetic/geometric start","schema":{"type":"string"}},{"name":"step","in":"query","required":false,"description":"arithmetic step","schema":{"type":"string"}},{"name":"ratio","in":"query","required":false,"description":"geometric ratio","schema":{"type":"string"}},{"name":"base","in":"query","required":false,"description":"powers base","schema":{"type":"string"}}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"count":10,"terms":[0,1,1,2,3,5,8,13,21,34],"sequence":"fibonacci"},"meta":{"timestamp":"2026-06-03T09:25:02.726Z","request_id":"3a8c06b7-ee2c-4a01-ad7b-259f14fc5519"},"status":"ok","message":"Generate a sequence","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/meta":{"get":{"operationId":"get_v1_meta","tags":["Meta"],"summary":"Spec","description":"","parameters":[],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"name":"Number Sequences API","notes":"Terms beyond 2^53 are returned as decimal strings to stay exact. Membership uses closed forms for primes, squares, cubes, triangular, pentagonal and Fibonacci; other sequences are searched up to a large cap. Nothing is stored.","version":"v1","endpoints":[{"path":"/v1/generate","params":{"base":"powers base","step":"arithmetic step","count":"how many terms (default 10, max 1000)","ratio":"geometric ratio","start":"arithmetic/geometric start","sequence":"fibonacci, lucas, primes, triangular, square, cube, factorial, catalan, pentagonal, tetrahedral, arithmetic, geometric, powers"},"returns":"the sequence terms"},{"path":"/v1/contains","params":{"value":"the integer to test","sequence":"the sequence name"},"returns":"whether the number is in the sequence (and its index when known)"},{"path":"/v1/meta","params":[],"returns":"this document"}],"description":"Generate famous integer sequences and test membership, with exact big-integer maths. The generate endpoint returns the first N terms of a sequence — fibonacci, lucas, primes, triangular, square, cube, factorial, catalan, pentagonal, tetrahedral, plus parameterised arithmetic (start, step), geometric (start, ratio) and powers (base). The contains endpoint tells you whether a given number belongs to a sequence (is 233 a Fibonacci number? is 21 triangular? is 97 prime?), using closed-form tests where they exist. Large terms are returned exactly as strings so nothing overflows. Pure local, no key."},"meta":{"timestamp":"2026-06-03T09:25:02.833Z","request_id":"75089189-e1f2-4ed7-a6d5-270599e518e0"},"status":"ok","message":"Meta","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}}},"x-oanor-pricing":[{"slug":"free","name":"Free","price_cents_month":0,"monthly_call_quota":2835,"rps_limit":2,"hard_limit":true},{"slug":"starter","name":"Starter","price_cents_month":435,"monthly_call_quota":12350,"rps_limit":8,"hard_limit":true},{"slug":"pro","name":"Pro","price_cents_month":2425,"monthly_call_quota":174500,"rps_limit":20,"hard_limit":true},{"slug":"mega","name":"Mega","price_cents_month":6225,"monthly_call_quota":915000,"rps_limit":50,"hard_limit":true}],"x-oanor-marketplace-url":"https://www.oanor.com/api/sequences-api"}