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A242076
Numbers k for which (2^k + 1)/F is prime where F is a Fermat number.
0
3, 5, 6, 7, 11, 12, 13, 17, 19, 20, 23, 28, 31, 40, 43, 61, 79, 92, 96, 101, 104, 127, 148, 167, 191, 199, 313, 347, 356, 596, 692, 701, 1004, 1228, 1268, 1709, 2617, 3539, 3824, 5807, 10501, 10691, 11279, 12391, 14479, 42737
OFFSET
1,1
COMMENTS
Conjecture: 6 is the only term whose prime factorization contains a single 2.
The largest odd divisor of each term is prime, that is, subsequence of A038550. - J. Lowell, Apr 13 2018
This sequence contains only certain terms from A092559 and certain multiples of 32. - Jon E. Schoenfield, Apr 18 2018 [with thanks to J. Lowell]
EXAMPLE
12 is a term because (2^12 + 1)/17 = 241, a prime number.
PROG
(Sage)
def a(n):
num = 2^n + 1
k = 0
while k < log(n, 2):
if num % (2^(2^k) + 1) == 0 and is_prime(Integer(num/(2^(2^k)+1))):
return True
k = k + 1
return False # Ralf Stephan, May 15 2014
CROSSREFS
Cf. A000215 (Fermat numbers), A066263.
Sequence in context: A324511 A360008 A092559 * A349897 A064728 A046839
KEYWORD
nonn,more
AUTHOR
J. Lowell, May 03 2014
EXTENSIONS
More terms from Ralf Stephan, May 15 2014
a(40)-a(46) from Jon E. Schoenfield, Apr 14 2018
Wrong property removed by J. Lowell, Apr 14 2018
STATUS
approved