ScorpTech x402 Tools

Pell Lucas

pell_lucas

Read-onlyIdempotent

The nth companion Pell-Lucas number. Q0 and Q1 are both 2, and later terms use the Pell recurrence. 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-lucas

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_lucas"
  }
}

Input Schema

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

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4/5.0

Behavior4/5

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

Annotations already declare the tool as read-only, idempotent, open-world, and non-destructive, and the description adds valuable behavioral details: zero is rejected, results beyond 15 digits are returned as decimal strings, and calls cost $0.001 USDC via x402. The 'zero is rejected' phrasing is slightly ambiguous about whether it refers to n=0 or modulus=0, which keeps this from a 5.

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

Conciseness5/5

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

The description is short and front-loaded: it gives the sequence definition first, then constraints, output format, and payment/API details. Every sentence contributes operational or mathematical context.

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

Completeness4/5

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

With no output schema, the description does well by explaining the sequence, valid range, modulus behavior, rejection behavior, and large-value return format. It remains slightly incomplete about small-value return type and the exact modulus input format.

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

Parameters3/5

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

Schema description coverage is 0%, so the description must carry parameter meaning. It usefully states that n runs 0–8192 and that the optional modulus reduces the term, but it does not explain the modulus string format, maximum length, or precise return semantics when mod is used.

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?

The description opens with a precise mathematical object: 'The nth companion Pell-Lucas number,' and reinforces it with initial values Q0=Q1=2 and the Pell recurrence. This distinguishes it from generic Pell or Lucas siblings without needing to explicitly name them.

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 description defines the sequence and valid n range, but it does not say when an agent should choose this tool over siblings like pell, pell_sum, or lucas. Usage is implied by the purpose, but no alternatives or exclusions are discussed.

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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