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
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
KEYWORD
nonn,more
AUTHOR
Amiram Eldar and Thomas Ordowski, Jun 20 2021
EXTENSIONS
a(22) from Max Alekseyev, Sep 11 2023
STATUS
approved