ScorpTech x402 API

Pell

pell

Read-onlyIdempotent

The nth Pell number. P0 is 0, P1 is 1, and each later term is twice the previous one plus the one before that. An optional modulus reduces the term, and zero is rejected. n runs from 0 to 8192. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/pell

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "n": "<n>"
    },
    "name": "pell"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes
`mod`	No

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.4/5.0

Behavior5/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations only cover the safety profile (readOnly/idempotent/non-destructive); the description adds substantial context on top: modulus reduces the term, mod=0 is rejected, n is bounded to 0-8192, values past 15 digits are returned as a decimal string, plus pricing ($0.001 USDC) and the HTTPS alternative endpoint.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loaded with the core definition, then parameters, output format, and operational details. Every sentence is relevant, though the price and HTTPS endpoint metadata are operational noise for pure computation use.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

No output schema exists, yet the description discloses the return representation (integer vs decimal string past 15 digits), the valid input domain, and the modulus edge case — enough for an agent to call and interpret results correctly.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

With 0% schema description coverage the description must carry the load, and it does: it bounds n (0 to 8192), identifies mod as an optional modulus that reduces the result, and states a zero modulus is rejected. It adds real meaning beyond the type/pattern constraints in the schema, though it doesn't explain mod's string-vs-integer representation.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

Specific verb+resource ('The nth Pell number') with the exact recurrence defined, so an agent can distinguish it from pell_lucas, pell_sum, pell_compose, or neg_pell without opening any schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The recurrence definition implicitly scopes this to single-term lookups, but there is no explicit statement of when to prefer it over siblings like pell_lucas or pell_sum, nor any when-not guidance. Usage is inferable, not stated.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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