bibkey: oeis2026a036236 authors: OEIS Foundation Inc. year: 2026 title: OEIS A036236 doi: null url: https://oeis.org/A036236 claim: The entry records the least-prime-factor proof that two to the n is never one modulo n for n greater than one, and the residue formula at powers of three. strata_touched:

• D5/S3/Arith/Congruence/PowerResidueRecursionFour license: citation-only triage: anchor

OEIS A036236

The entry is the least inverse of A015910, the sequence 2^n mod n: it asks for the least positive index producing each residue, with zero indicating that no such index exists. Max Alekseyev’s comment proves the exclusion of residue one using the least prime divisor and multiplicative order. A formula credited to Farideh Firoozbakht gives the residue at n = 3^k as 3^k - 1. These are known ingredients of the A374911 proof, not results whose originality is claimed by this implementation.

Verified locator

url: https://oeis.org/A036236

The worker read the full OEIS text entry on 2026-09-10, following its link from A015910. The relevant locations are Alekseyev’s COMMENTS argument and Firoozbakht’s FORMULA. There is no DOI for this entry; the bibliographic year here is the access year for the continuously maintained entry.

Formal use

The module proves the exclusion using Mathlib’s order divisibility and least-prime-factor API. It obtains the powers-of-three residue formula from Mathlib’s addition form of lifting the exponent. Both helper statements are private prerequisites of the recursive classification.