{"uid":"cap_n6lS3o_PB62RyIVgirxbu","slug":"numora-sequence-generation-api-66186875","name":"Numora Sequence Generation API","description":"100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.","url":"https://numormo.vercel.app/api/generate/sequence","method":"POST","headers":{},"bodySchema":{"type":"object","required":["n","rule"],"properties":{"n":{"type":"integer"},"rule":{"type":"string","description":"Recurrence rule (e.g., 'a[n] = 2*a[n-1] + 1')"},"initial":{"type":"array"}}},"responseSchema":{"type":"object","required":["success","result","computation"],"properties":{"result":{"type":"object","description":"Computation result varies by endpoint"},"success":{"type":"boolean","description":"Always true on success"},"computation":{"type":"string","description":"Human-readable description of what was computed"}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"registry","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_FYMOyrINQu8HjUjxTty9y","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":null,"unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Generates mathematical sequences of specified length using a user-defined recurrence rule and optional initial conditions","exampleAgentPrompt":"Generate the first 15 terms of the sequence defined by the rule a[n] = 2*a[n-1] + 1, starting with initial values [1, 2].","exampleUseCases":[{"title":"Fibonacci variant sequence generation","prompt":"Give me the first 20 terms of a sequence where a[n] = a[n-1] + a[n-2], starting from [0, 1]."},{"title":"Exponential growth sequence modeling","prompt":"Compute 10 terms of the recurrence a[n] = 3*a[n-1] with initial value [2], so I can analyze exponential growth patterns."},{"title":"Custom linear recurrence for puzzle design","prompt":"Generate 25 terms of the sequence a[n] = a[n-1] + a[n-2] + a[n-3] starting with [1, 1, 2] — I need it for a number puzzle I'm building."}],"resultDescription":"Returns a JSON object with a boolean success flag, a result object containing the computed sequence terms, and a computation string describing in human-readable form what was calculated.","failureModes":["Invalid or unparseable recurrence rule expression returns an error","n not provided or non-integer causes a validation failure","Initial values array too short for the recurrence rule's look-back depth","Division by zero or undefined operations within the rule expression","Malformed JSON body returns a 400-level error"],"whenToPreferThis":"Choose this endpoint when you need to generate a custom mathematical sequence from an arbitrary recurrence relation with full control over initial conditions and length. It requires no external dependencies and is ideal for pure math use cases — number theory exploration, algorithm seeding, pattern analysis, or educational sequence generation — where you want deterministic, serverless computation paid per-call via x402 micropayments.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T00:53:52.696Z","isFirstParty":false}