%I #75 Jun 09 2022 21:56:34
%S 3,5,6,7,11,12,13,17,19,20,23,28,31,40,43,61,79,92,96,101,104,127,148,
%T 167,191,199,313,347,356,596,692,701,1004,1228,1268,1709,2617,3539,
%U 3824,5807,10501,10691,11279,12391,14479,42737
%N Numbers k for which (2^k + 1)/F is prime where F is a Fermat number.
%C Conjecture: 6 is the only term whose prime factorization contains a single 2.
%C The largest odd divisor of each term is prime, that is, subsequence of A038550. - _J. Lowell_, Apr 13 2018
%C This sequence contains only certain terms from A092559 and certain multiples of 32. - _Jon E. Schoenfield_, Apr 18 2018 [with thanks to _J. Lowell_]
%e 12 is a term because (2^12 + 1)/17 = 241, a prime number.
%o (Sage)
%o def a(n):
%o num = 2^n + 1
%o k = 0
%o while k < log(n, 2):
%o if num % (2^(2^k) + 1) == 0 and is_prime(Integer(num/(2^(2^k)+1))):
%o return True
%o k = k + 1
%o return False # _Ralf Stephan_, May 15 2014
%Y Cf. A000215 (Fermat numbers), A066263.
%K nonn,more
%O 1,1
%A _J. Lowell_, May 03 2014
%E More terms from _Ralf Stephan_, May 15 2014
%E a(40)-a(46) from _Jon E. Schoenfield_, Apr 14 2018
%E Wrong property removed by _J. Lowell_, Apr 14 2018