bibkey: cloitre2002a072872
authors: Benoit Cloitre
year: 2002
title: "OEIS A072872, a(n) is the smallest positive number k such that n divides 2^k - k"
doi: null
url: https://oeis.org/A072872
claim: "a(n) is the smallest positive number k such that n divides 2^k - k. If n is a power of 2, a(n) = n. Conjecture : if n > 47, a(n) < prime(n). - _Benoit Cloitre_, Jul 28 2002"
strata_touched:
  - D5/S3/Arith/Congruence/CloitrePowerMinusIndexPrimeBoundRefutation
license: citation-only
triage: anchor

OEIS A072872

The NAME of A072872 defines the sequence as:

a(n) is the smallest positive number k such that n divides 2^k - k

The COMMENTS state:

If n is a power of 2, a(n) = n. Conjecture : if n > 47, a(n) < prime(n). - Benoit Cloitre, Jul 28 2002

The formalization records the sequence definition, the literal prime-index upper-bound conjecture, and a certified counterexample. It makes no general existence claim for the defining set.

Verified locator

• URL: https://oeis.org/A072872
• NAME (verbatim): a(n) is the smallest positive number k such that n divides 2^k - k
• COMMENTS (verbatim): If n is a power of 2, a(n) = n. Conjecture : if n > 47, a(n) < prime(n). - Benoit Cloitre, Jul 28 2002