ScorpTech x402 Tools

Entringer

entringer

Read-onlyIdempotent

The Entringer number E(n, k). E(1, 1) is 1, and E(n, k) = E(n, k-1) + E(n-1, n-k). E(5, 2) is 10, and E(6, 3) is 46. The last entry E(n, n) is the zigzag number a(n). n and k run from 1 to 40, and k must not pass n. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/entringer

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>",
      "k": "<k>"
    },
    "name": "entringer"
  }
}

Input Schema

Name	Required	Description	Default
`k`	Yes
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.3/5.0

Behavior4/5

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

Annotations already declare readOnlyHint, idempotentHint, openWorldHint, and destructiveHint=false, so the safety profile is clear. The description adds useful behavioral context: pricing at $0.001 USDC per successful call, x402/Solana payment, and an equivalent HTTPS endpoint.

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 front-loaded with the mathematical definition, followed by examples, constraints, and payment details. Every sentence adds useful information without unnecessary repetition.

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?

For a simple two-parameter mathematical calculator with no output schema, the description is nearly complete: it gives the formula, domain, examples, and access/payment details. It could explicitly state the return type and error behavior when k > n, but the essential calling information is present.

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

Parameters5/5

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

Although schema description coverage is 0%, the description compensates by explaining that n and k run from 1 to 40 and that k must not exceed n, a constraint not encoded in the schema. The recurrence and worked examples further clarify how the parameters define the result.

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 explicitly defines the tool as computing the Entringer number E(n, k), gives the recurrence, and notes that E(n, n) is the zigzag number a(n). This clearly distinguishes it from sibling sequence tools, including euler_zigzag.

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?

Usage is implied by the precise mathematical definition, but the description does not explicitly state when to choose this tool over related sequence tools or when not to use it. The constraints on n and k are helpful but are parameter validity rules rather than usage guidance.

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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