{"id":"lucas-number","version":"1.0.0","description":"Compute the Lucas number at a zero-based index and return its exact decimal string.","supported_operations":["lucas number 90","compute nth lucas number","exact lucas sequence value","lucas number at index","calculate lucas without rounding","what is the 100th lucas number","zero based lucas lookup"],"unsupported_operations":["negative-index sequence extensions","floating-point approximations","unbounded sequence generation"],"semantics":["L(0)=2, L(1)=1, and L(n)=L(n-1)+L(n-2).","The index is zero-based and the result is an unsigned base-10 string.","Standard version: OEIS A000032 (live entry retrieved 2026-11-05; NAME, initial terms, OFFSET 0,1); stable source URL: https://oeis.org/A000032."],"limits":{"max_input_bytes":64,"max_index":10000,"max_digits":2091,"max_iterations":14,"max_output_bytes":2300},"pricing":{"status":"unpriced","charge_usd":null},"input_schema":{"type":"object","additionalProperties":false,"required":["index"],"properties":{"index":{"type":"integer","minimum":0,"maximum":10000}}},"output_schema":{"type":"object","additionalProperties":false,"required":["index","value","standard_version"],"properties":{"index":{"type":"integer","minimum":0,"maximum":10000},"value":{"type":"string","minLength":1,"maxLength":2091,"pattern":"^[0-9]+$"},"standard_version":{"type":"string","minLength":1,"maxLength":120}}},"examples":[{"input":{"index":10},"output":{"index":10,"value":"123","standard_version":"OEIS A000032 (live entry retrieved 2026-11-05; NAME, initial terms, OFFSET 0,1)"}},{"input":{"index":90},"output":{"index":90,"value":"6440026026380244498","standard_version":"OEIS A000032 (live entry retrieved 2026-11-05; NAME, initial terms, OFFSET 0,1)"}}],"execute_url":"/v1/tools/lucas-number/versions/1.0.0/execute"}