[seqfan] A175942

Tomasz Ordowski tomaszordowski at gmail.com
Thu Jun 3 13:10:41 CEST 2021

Dear readers,

  I noticed (without full proof) that these are ...
Numbers n such that 2^(n-1) == 3n+1 (mod 3(n-1)n).
  Problem: are there infinitely many such numbers?
Such known composites are of the form (2^(2k+1)+1)/3,
where k is in A303009. See last comment on A175942:
https://oeis.org/A175942 (see the equivalent definitions).
  These four Carmichael numbers n for which D_{n-1} = 6n,
(*) 310049210890163447 and 18220439770979212619, nor (**)
326454636194318621086787 and 5271222682189523956137705530039,
are not (unknown) composite terms of the title sequence A175942.
Note that many primes p in A175942 are such that D_{p-1} = 6p,
A092307: https://oeis.org/history/view?seq=A092307&v=28
  It seems that A175942 contains all safe primes p <> 7,
A005385: https://oeis.org/A005385
I am asking for a (dis)proof,
(a counterexample).

Best regards,

Thomas Ordowski
( ) These are composite numbers n such that D_{n-1} = 6n,
where D_k is the denominator of Bernoulli number B_k,
found by: Amiram Eldar (*) & Daniel Suteu (**).

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