Hopi

Sequence solver

hopi_sequence_solver

Read-onlyIdempotent

Find the rule behind a list of numbers and predict the next terms. Checks constant, arithmetic and geometric sequences, polynomials up to degree 5 by finite differences, sequences whose differences are geometric (such as 2^n - 1), order-2 linear recurrences (Fibonacci, Lucas, Pell and others), Catalan numbers, alternating signs, reciprocals, repeating cycles and two interleaved sequences. All arithmetic is exact, using BigInt fractions, so decimals such as 0.1 and fractions such as 1/3 stay exact. Give 3 to 40 terms. Every number comes back as a string. spareTerms is how many of your terms the rule did not need to pin itself down: 0 means it needed them all, so treat the answer as a guess. alternatives lists other rules that also fit, including the polynomial through every term, which always exists. When nothing fits, found is false, rule is "No simple rule found" and nextTerms is empty. Source: https://hopi.co.uk/sequence-solver/

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": {
      "terms": "<terms>"
    },
    "name": "hopi_sequence_solver"
  }
}

Input Schema

Name	Required	Description	Default
`count`	No	How many next terms to predict, from 1 to 20 (default 5)
`terms`	Yes	3 to 40 terms in order, as an array such as [1, 3, 7, 15, 31] or as text such as "1, 3, 7, 15, 31". Whole numbers, decimals and fractions such as "1/3" all work. In text separated by spaces, a comma followed by 3 digits inside a number ("1,000, 2,000") is a thousands separator; text with no spaces is split at every comma. Send whole numbers above 9,007,199,254,740,991 as strings to keep every digit

Output Schema

Name	Required	Description
`rule`	No
`found`	No
`method`	No
`formula`	No
`oeisUrl`	No
`summary`	Yes
`nextTerms`	No
`termsUsed`	No
`source_url`	Yes	The tool's page on hopi.co.uk (cite or open to check the figure)
`spareTerms`	No
`alternatives`	No
`differenceTable`	No

Schema Changelog

Changes observed during successful MCP inspections.

AddedNov 1, 2026

TDQS

A4.4/5.0

Behavior5/5

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

Goes well beyond the readOnly/idempotent annotations: it discloses exact BigInt arithmetic semantics, that all numbers are returned as strings, the meaning of spareTerms and alternatives, and the exact failure shape (found=false, rule 'No simple rule found', empty nextTerms). This is unusually rich disclosure for a computation tool.

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?

Front-loads the purpose, then packs rule families, precision guarantees, and output semantics into short clauses with no filler. It runs long and dense, but each sentence carries distinct information; only the source URL is dispensable.

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

Completeness5/5

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

Given two parameters, an output schema, and full annotations, the description covers input constraints, precision behavior, output interpretation, ambiguity handling, and the no-match case. An agent has everything needed to call it and to read the result correctly.

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?

Schema description coverage is 100% and the schema already documents terms formatting, thousands separators, and the count range, so the baseline is 3. The description reinforces the 3–40 term bound and the big-integer-as-string rule but adds nothing about the count parameter or formatting beyond what the schema states.

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?

States a specific verb+resource (find the rule behind a list of numbers, predict next terms) and then enumerates the exact rule families it recognizes, which no sibling tool touches. An agent can identify this as the sequence-extrapolation tool without ambiguity.

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

Usage Guidelines4/5

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

Gives concrete operating context: give 3 to 40 terms, and a clear interpretation rule for spareTerms=0 ('treat the answer as a guess') plus the fallback 'When nothing fits, found is false'. It does not name a sibling alternative, but no sibling here plausibly competes, so the missing routing is minor.

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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