A096820 Numbers k such that 2^k - 21 is prime.

5, 6, 7, 9, 11, 13, 14, 21, 23, 41, 46, 89, 110, 389, 413, 489, 869, 1589, 1713, 2831, 10843, 11257, 16949, 24513, 39621, 43349, 62941, 96094, 139237, 145289, 264683, 396790, 420694, 439931, 659589, 783893, 840203, 944561

Offset: 1

Author

Labos Elemer, Jul 13 2004

Keywords

• nonn
• more

Comments

Similar to A057202 (which allows negative primes): this sequence is obtained by dropping the first four terms of A057202. - Joerg Arndt, Oct 05 2012

Examples

			k = 5: 32 - 21 = 11 is prime.
k = 7: 128 - 21 = 107 is prime.
		

Links

• Henri Lifchitz and Renaud Lifchitz, Search for 2^n-21, 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), A096819 (d=19), this sequence (d=21), A057220 (d=23), A356826 (d=29).

Programs

Mathematica

Select[Range[5,20000],PrimeQ[2^#-21]&] (* Vladimir Joseph Stephan Orlovsky, Feb 27 2011 *)

Sage

def is_A096820(n):
    t = 2^n-21
    return t > 1 and is_prime(t)
def A096820_list(up_to):
    return [n for n in range(up_to) if is_A096820(n)]
A096820_list(100)  # Peter Luschny, Oct 04 2012

Extensions

a(23)-a(24) from Max Alekseyev, a(25) from Donovan Johnson, a(26)-a(28) from Henri Lifchitz, a(29)-a(30) from Lelio R Paula, added by Max Alekseyev, Feb 10 2012

a(31)-a(32) from Lelio R Paula, added by Max Alekseyev, Oct 24 2013

a(33)-a(34) found by Lelio R Paula, a(35)-a(38) found by Stefano Morozzi, added by Elmo R. Oliveira, Nov 24 2023