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

Annotations already declare readOnlyHint=true, idempotentHint=true and openWorldHint=false, so the agent knows this is a safe, repeatable, closed lookup. The description adds only that the content is a static vocabulary list, which mildly reinforces the read-only nature but discloses nothing about the form or depth of the returned reference material.

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

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

A single front-loaded sentence with a precise colon-delimited inventory; no filler, no restatement of the title, and the three categories align directly with the enum values.

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

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

An output schema exists, so return values need no explanation, and the single enum parameter is fully documented. It is complete for its scope, though one clause pointing at the sequence-oriented siblings would make the routing unambiguous.

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

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

Schema description coverage is 100% and the enum's own description enumerates keywords, search_syntax, and identifiers in the same terms the description uses. The description therefore restates schema content rather than adding new semantics, so the baseline 3 applies.

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

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

States a specific verb (look up) and resource (OEIS vocabulary/reference material) and immediately scopes it to what 'the other tools' consume, which separates it from sequence-retrieval siblings like oeis_get_sequence and oeis_search_sequences. It does not name a sibling explicitly, so it falls just short of a 5.

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

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

The phrase 'used by the other tools' implies this is a supporting reference to consult when interpreting keywords or search syntax from those tools, but it never states when to call it versus those siblings or any prerequisite/exclusion. Usage is inferable rather than explicit.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.