A096818 Numbers k such that 2^k - 13 is prime.

4, 5, 9, 13, 17, 57, 105, 137, 3217, 3229, 4233, 6097, 8757, 11457, 12073, 15425, 40117, 45357, 334809, 1509037

Offset: 1

Author

Labos Elemer, Jul 13 2004

Keywords

• nonn
• more

Comments

Except the first term 4, all terms are odd since for even k, 2^k - 13 is divisible by 3.

Examples

			k = 5: 32 - 13 = 19 is prime.
		

Links

• F. Firoozbakht and M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1.
• Henri Lifchitz and Renaud Lifchitz, Search for 2^n-13, PRP Top Records.

Crossrefs

Cf. A096502.

Cf. Sequences of numbers k such that 2^k - d is prime: A000043 (d=1), A050414 (d=3), A059608 (d=5), A059609 (d=7), A059610 (d=9), A096817 (d=11), this sequence (d=13), A059612 (d=15), A059611 (d=17), A096819 (d=19), A096820 (d=21), A057220 (d=23), A356826 (d=29).

Programs

Mathematica

Select[Range[4,20000],PrimeQ[2^#-13]&] (* Vladimir Joseph Stephan Orlovsky, Feb 27 2011 *)

Extensions

a(16) from Max Alekseyev, a(17)-a(18) from Henri Lifchitz, a(19) from Lelio R Paula, added by Max Alekseyev, Feb 09 2012

a(20) found by Stefano Morozzi, added by Elmo R. Oliveira, Nov 17 2023