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IBM

MCP Math Server

by IBM

kaprekar_sequence

Generate Kaprekar sequences for numbers by iteratively rearranging digits to find fixed points in arithmetic operations.

Instructions

Generate Kaprekar sequence for a number with given digit count. (Domain: arithmetic, Category: iterative_sequences)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
digitsYes
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 mentions 'iterative_sequences' in the category, hinting at iterative behavior, but doesn't specify details like convergence criteria, output format (e.g., list of numbers), error handling for invalid inputs, or computational limits. This leaves significant gaps for a tool that likely involves iterative calculations.

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?

The description is concise with a single sentence and domain/category tags, making it easy to parse. However, it's under-specified rather than optimally concise—it could benefit from a bit more detail without becoming verbose. The structure is front-loaded with the core purpose.

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 no annotations, 0% schema coverage, no output schema, and two parameters, the description is incomplete. It doesn't explain the iterative process, output format, error conditions, or relation to sibling tools. For a mathematical sequence generator, more context is needed to use it effectively.

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%, so the schema provides no parameter details. The description only mentions 'a number with given digit count', which partially explains 'n' and 'digits' but lacks specifics: what ranges are valid? Are digits the length of n? Does n need to be positive? It adds minimal meaning beyond the bare parameter names.

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

Purpose3/5

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

The description states the tool generates a Kaprekar sequence for a number with given digit count, which provides a basic purpose. However, it's vague about what a Kaprekar sequence entails (e.g., iterative rearrangement of digits) and doesn't distinguish from siblings like 'kaprekar_numbers' or 'kaprekar_constant', which are related but different operations. The domain/category tags add context but don't clarify the specific behavior.

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?

No guidance is provided on when to use this tool versus alternatives. The description doesn't mention prerequisites (e.g., valid input ranges), exclusions, or comparisons to sibling tools like 'kaprekar_numbers' (which might list Kaprekar numbers) or 'kaprekar_constant' (which might compute the constant). Usage is implied only by the name and basic description.

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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