{"uid":"cap_lCCi_K3PC2HUSr_wtxFgP","slug":"numora-sequence-generation-api-aced7ae1","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://numomo.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_uNHSEWoWipmF4UkrIhaW_","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 length n using a user-defined recurrence rule and optional initial conditions","exampleAgentPrompt":"Generate the first 15 terms of the sequence defined by the recurrence rule a[n] = 2*a[n-1] + 3 starting with initial values [1, 2].","exampleUseCases":[{"title":"Fibonacci-style sequence generation","prompt":"Can you generate the first 20 terms of a sequence where a[n] = a[n-1] + a[n-2], starting from initial values [0, 1]?"},{"title":"Exponential growth sequence modeling","prompt":"I need the first 10 terms of a sequence with the rule a[n] = 3*a[n-1] and starting value [2], so I can model exponential growth in a spreadsheet."},{"title":"Custom recurrence for algorithm testing","prompt":"Generate 25 terms of the sequence a[n] = a[n-1] + 2*a[n-2] - 1 with initial values [0, 1] so I can verify my recursive algorithm implementation."}],"resultDescription":"Returns a JSON object with a 'success' boolean, a 'result' object containing the generated sequence terms, and a 'computation' string that describes in human-readable form what was computed (e.g., which rule was applied and how many terms were generated).","failureModes":["Invalid or unparseable recurrence rule expression returns an error","n is zero or negative, resulting in an empty or invalid sequence","Initial values array has fewer elements than required by the recurrence depth","Malformed JSON body causes a 400-level error","Rule references undefined variables or uses unsupported syntax"],"whenToPreferThis":"Choose this endpoint when you need to generate a mathematically defined sequence from a recurrence relation or formula, especially when you want zero external dependencies and deterministic pure-math computation. Prefer this over custom code execution environments when the task is simply evaluating a recurrence rule for a fixed number of terms, and when micropayment-per-call billing ($0.02 USDC) fits the usage pattern better than a subscription.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T12:46:57.201Z","isFirstParty":false}