# Numora Sequence Generation API

> Numora Sequence Generation API is a paid API for AI agents from numorapoi.orbonomy.xyz, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-23).

Generates mathematical sequences of arbitrary length using custom recurrence rules and initial conditions

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/generate/sequence?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-23
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-sequence-generation-api-4fbdb9e6
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_vW-3xh6aMPjsewU5sF223

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-4fbdb9e6 -d '<json body>'
```

Example prompt: Generate the first 15 terms of the sequence defined by the recurrence rule a[n] = 2*a[n-1] + a[n-2], starting with initial values [1, 1].

## When to prefer this

Use this endpoint when you need to generate a sequence of numbers from a custom recurrence relation or mathematical rule without relying on external libraries or services. Ideal for AI agents needing deterministic, pure-math sequence generation with no side effects. Prefer this over general-purpose code execution when you want a lightweight, paid-per-call micro-service that handles the math computation for you.

## Known failure modes

- Invalid or unparseable recurrence rule string — returns error indicating rule syntax issue
- n is zero or negative — may return empty result or validation error
- Insufficient initial values provided for the recurrence depth — returns error about missing initial conditions
- Malformed JSON body — returns 400 bad request
- Payment not attached or insufficient — returns 402 Payment Required

## 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 'success' boolean, a 'result' object containing the generated sequence terms, and a 'computation' string describing in human-readable language what was computed (e.g. the rule applied and number of terms generated).

## 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-4fbdb9e6/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numorapoi.orbonomy.xyz](https://www.zero.xyz/host/numorapoi.orbonomy.xyz/llms.txt)