A096819 Numbers k such that 2^k - 19 is prime.

5, 7, 11, 15, 19, 21, 31, 39, 67, 69, 85, 157, 171, 191, 255, 291, 379, 3669, 4551, 9531, 13119, 14211, 20647, 233965, 337267, 534429, 535415, 816039, 991715

Offset: 1

Author

Labos Elemer, Jul 13 2004

Keywords

• nonn
• more

Comments

All terms are odd since for even k, 2^k - 19 is divisible by 3.

a(26) > 5*10^5. - Tyler NeSmith, Apr 16 2022

Examples

			2^7 - 19 = 128 - 19 = 109, a prime, so 7 is a term of the sequence.
		

Links

• Henri Lifchitz and Renaud Lifchitz, Search for 2^n-19, 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), A096818 (d=13), A059612 (d=15), A059611 (d=17), this sequence (d=19), A096820 (d=21), A057220 (d=23), A356826 (d=29).

Programs

Mathematica

Select[Range[5,20000],PrimeQ[2^#-19]&] (* Vladimir Joseph Stephan Orlovsky, Feb 27 2011*)

Extensions

a(22)-a(23) from Max Alekseyev, Feb 10 2012

a(24)-a(25) from Lelio R Paula, added by Max Alekseyev, Oct 24 2013

a(26)-a(29) found by Stefano Morozzi, added by Alois P. Heinz, Aug 29 2022