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A242076 Numbers k for which (2^k + 1)/F is prime where F is a Fermat number.

%I A242076 #75 Jun 09 2022 21:56:34
%S A242076 3,5,6,7,11,12,13,17,19,20,23,28,31,40,43,61,79,92,96,101,104,127,148,
%T A242076 167,191,199,313,347,356,596,692,701,1004,1228,1268,1709,2617,3539,
%U A242076 3824,5807,10501,10691,11279,12391,14479,42737
%N A242076 Numbers k for which (2^k + 1)/F is prime where F is a Fermat number.
%C A242076 Conjecture: 6 is the only term whose prime factorization contains a single 2.
%C A242076 The largest odd divisor of each term is prime, that is, subsequence of A038550. - _J. Lowell_, Apr 13 2018
%C A242076 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 A242076 12 is a term because (2^12 + 1)/17 = 241, a prime number.
%o A242076 (Sage)
%o A242076 def a(n):
%o A242076     num = 2^n + 1
%o A242076     k = 0
%o A242076     while k < log(n, 2):
%o A242076         if num % (2^(2^k) + 1) == 0 and is_prime(Integer(num/(2^(2^k)+1))):
%o A242076             return True
%o A242076         k = k + 1
%o A242076     return False          # _Ralf Stephan_, May 15 2014
%Y A242076 Cf. A000215 (Fermat numbers), A066263.
%K A242076 nonn,more
%O A242076 1,1
%A A242076 _J. Lowell_, May 03 2014
%E A242076 More terms from _Ralf Stephan_, May 15 2014
%E A242076 a(40)-a(46) from _Jon E. Schoenfield_, Apr 14 2018
%E A242076 Wrong property removed by _J. Lowell_, Apr 14 2018