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

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

Author

J. Lowell, May 03 2014

Keywords

• nonn
• more

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]

Examples

			12 is a term because (2^12 + 1)/17 = 241, a prime number.
		

Crossrefs

Cf. A000215 (Fermat numbers), A066263.

Programs

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

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