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IBM

MCP Math Server

by IBM

pronic_sequence

Generate the first n pronic numbers to explore figurate numbers in arithmetic sequences.

Instructions

Generate the first n pronic numbers. (Domain: arithmetic, Category: figurate_numbers)

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. It states the tool generates numbers but lacks details on behavior: no information on output format (e.g., list, array), error handling (e.g., for negative n), performance, or limits. The description is minimal and doesn't compensate for the absence of annotations.

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 highly concise and front-loaded: a single sentence directly states the tool's purpose, followed by domain/category in parentheses. There is no wasted text, and every part serves to clarify the tool's function efficiently.

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 complexity (a sequence generator with one parameter), no annotations, no output schema, and 0% schema coverage, the description is incomplete. It doesn't explain what pronic numbers are, the output format, or any behavioral aspects, making it inadequate for full understanding despite its conciseness.

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

Parameters2/5

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

Schema description coverage is 0%, and the description doesn't add any parameter semantics. It mentions 'n' implicitly ('first n pronic numbers') but doesn't explain what 'n' represents (e.g., count, integer > 0), its range, or constraints. With low schema coverage, the description fails to compensate, leaving parameters poorly documented.

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 first n pronic numbers.' It specifies the verb ('Generate') and resource ('pronic numbers') with a parameter constraint ('first n'). However, it doesn't explicitly differentiate from sibling tools like 'is_pronic_number' or 'pronic_sequence' (if present), which slightly limits its distinction.

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 ('figurate_numbers'), but offers no explicit instructions on context, prerequisites, or comparisons with sibling tools like 'is_pronic_number' or other sequence generators.

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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