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