%I
%S 1,3,9,13,17,19,31,33,37,43,65,79,115,129,187,223,367,403,535,763,835
%N Odd numbers k with (k1)/2 not prime such that p1  k1 or k1  p1 for every prime p  2^(k1)1.
%C Are there only finitely many such numbers? No more terms below 2217.
%C For those numbers k, if k <> 2^m + 1, then k == 1 (mod 6).
%t 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[#] &]
%Y Cf. A334797 (see comments section).
%K nonn,more
%O 1,2
%A _Amiram Eldar_ and _Thomas Ordowski_, Jun 20 2021
