# Numora Sequence Generation API

> Numora Sequence Generation API is a paid API for AI agents from numormo.vercel.app, paid per call via x402, $0.02/call, status unknown (last checked 2026-09-15).

Generates mathematical sequences of specified length using a user-defined recurrence rule and optional initial conditions

## Facts

- Endpoint: POST https://numormo.vercel.app/api/generate/sequence
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-sequence-generation-api-66186875
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_n6lS3o_PB62RyIVgirxbu

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-sequence-generation-api-66186875 -d '<json body>'
```

Example prompt: 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].

## When to prefer this

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.

## Known failure modes

- 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

## How this service works

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.

## Output

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.

## Request schema (JSON Schema)

```json
{
 "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"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "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"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-sequence-generation-api-66186875/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numormo.vercel.app](https://www.zero.xyz/host/numormo.vercel.app/llms.txt)