A345460 Odd numbers k with (k-1)/2 not prime such that p-1 | k-1 or k-1 | p-1 for every prime p | 2^(k-1)-1.

1, 3, 9, 13, 17, 19, 31, 33, 37, 43, 65, 79, 115, 129, 187, 223, 367, 403, 535, 763, 835, 2743

Offset

1,2

Comments

Are there only finitely many such numbers?

For those numbers k, if k <> 2^m + 1, then k == 1 (mod 6).

If other terms below 10^4 exist, they belong to the set { 6237, 7013, 7509, 7555, 7963, 8013, 8357, 8453, 9715, 9727, 9823 }. - Max Alekseyev, Sep 11 2023

Links

Table of n, a(n) for n=1..22.

Mathematica

q[k_] := AllTrue[FactorInteger[2^(k - 1) - 1][[;; , 1]], Divisible[k - 1, # - 1] || Divisible[# - 1, k - 1] &]; Select[Range[1, 230, 2], ! PrimeQ[(# - 1)/2] && q[#] &]

Crossrefs

Cf. A334797 (see comments section).

Sequence in context: A063791 A077791 A176393 * A239320 A243656 A363406

Adjacent sequences: A345457 A345458 A345459 * A345461 A345462 A345463

Keyword

nonn,more

Author

Amiram Eldar and Thomas Ordowski, Jun 20 2021

Extensions

a(22) from Max Alekseyev, Sep 11 2023

Status

approved