# Harmonic Number Sequence Generator

> Harmonic Number Sequence Generator is a paid API for AI agents from sovereign-x402-zeta.vercel.app, paid per call via x402, $0.001/call, status unknown (last checked 2026-10-11).

Generates a list of harmonic numbers (partial sums 1 + 1/2 + ... + 1/k for k=1..n) up to a specified limit n

## Facts

- Endpoint: POST https://sovereign-x402-zeta.vercel.app/api/v1/sequence/harmonic?utm_source=zero.xyz
- Price: $0.001/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-11
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/harmonic-number-sequence-generator-54ca222f
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_ymyQVmz9HHlHJiYym80v4

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 harmonic-number-sequence-generator-54ca222f -d '<json body>'
```

Example prompt: Can you generate the full list of harmonic numbers up to n=25 for me?

## When to prefer this

Use this endpoint when you need a pre-computed list of harmonic number values (partial sums of the harmonic series) up to some limit n, without implementing the computation yourself. Prefer it over general-purpose code execution when you want a simple, paid API call that returns the sequence directly. It complements the sibling prime-sequence endpoint on the same platform for mathematical sequence generation tasks.

## Known failure modes

- Missing or invalid limit n in request body — returns 400 error
- Non-integer or negative value for n — likely rejected or returns error
- Extremely large n may cause slow response or timeout
- Malformed JSON body — returns 400 or 422 error
- Payment not completed — returns 402 Payment Required

## How this service works

Generate a list of harmonic numbers (1 + 1/2 + ... + 1/n) up to a specified limit n.

## Output

A list of harmonic number values H(1), H(2), ..., H(n), where H(k) = 1 + 1/2 + 1/3 + ... + 1/k, computed as floating-point partial sums up to the specified limit n.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method",
    "bodyType",
    "body"
   ],
   "properties": {
    "body": {
     "type": "object",
     "properties": {},
     "additionalProperties": true
    },
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "POST",
      "PUT",
      "PATCH"
     ],
     "type": "string"
    },
    "bodyType": {
     "enum": [
      "json",
      "form-data",
      "text"
     ],
     "type": "string"
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object"
    }
   }
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/harmonic-number-sequence-generator-54ca222f/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from sovereign-x402-zeta.vercel.app](https://www.zero.xyz/host/sovereign-x402-zeta.vercel.app/llms.txt)