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IBM

MCP Math Server

by IBM

recaman_sequence

Generate the Recamán sequence up to a specified number of terms to explore this mathematical integer sequence through iterative computation.

Instructions

Generate the Recamán sequence up to n terms. (Domain: arithmetic, Category: iterative_sequences)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
Behavior2/5

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool generates a sequence, but does not describe output format (e.g., list of integers), error handling (e.g., for negative n), performance characteristics, or any side effects. For a tool with no annotations, this leaves significant gaps in understanding its behavior.

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 extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain and category in parentheses. There is no wasted text, and every part adds value (e.g., the domain/category provides additional context without redundancy).

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

Completeness2/5

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

Given the tool's complexity (generating a mathematical sequence), lack of annotations, no output schema, and low schema coverage, the description is insufficient. It does not explain what the Recamán sequence is, the output format, or any behavioral details. While conciseness is good, the description fails to provide enough context for an agent to use the tool effectively without external knowledge.

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?

The input schema has one parameter 'n' with 0% description coverage, so the schema provides no semantic information. The description adds meaning by specifying 'n terms', clarifying that 'n' is the number of terms to generate. However, it does not detail constraints (e.g., n must be positive) or provide examples, leaving some ambiguity. Given the low schema coverage, the description compensates partially but not fully.

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

Purpose4/5

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

The description clearly states the tool's purpose: 'Generate the Recamán sequence up to n terms.' It specifies the verb ('Generate'), resource ('Recamán sequence'), and scope ('up to n terms'), making it easy to understand. However, it does not explicitly differentiate from sibling tools, which include many other sequence generators (e.g., fibonacci_sequence, collatz_sequence), so it falls short of a perfect score.

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

Usage Guidelines2/5

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

The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('iterative_sequences'), but this is too vague to help an agent choose between similar tools like fibonacci_sequence or collatz_sequence. There are no explicit when/when-not instructions or named alternatives.

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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