A102633 Numbers k such that 2^k + 11 is prime.

1, 3, 5, 7, 9, 15, 23, 29, 31, 55, 71, 77, 297, 573, 1301, 1555, 1661, 4937, 5579, 6191, 6847, 6959, 19985, 26285, 47093, 74167, 149039, 175137, 210545, 240295, 306153, 326585, 345547

Offset: 1

Author

Lei Zhou, Jan 20 2005

Keywords

• nonn
• hard
• more

Comments

a(34) > 5*10^5. - Robert Price, Aug 26 2015

For numbers k in this sequence, 2^(k-1)*(2^k+11) has deficiency 12 (see A141549). All terms are odd since 4^n+11 == 1+2 == 0 (mod 3). - M. F. Hasler, Jul 18 2016

Examples

			k = 1: 2^1 + 11 = 13 is prime.
k = 3: 2^3 + 11 = 19 is prime.
k = 2: 2^2 + 11 = 15 is not prime.
		

Links

• Henri Lifchitz and Renaud Lifchitz (Editors), Search for 2^n+11, PRP Top Records.
• Lei Zhou, Between 2^n and primes. [broken link]

Crossrefs

Cf. A094076, A141549.

Cf. A019434 (primes 2^k+1), A057732 (2^k+3), A059242 (2^k+5), A057195 (2^k+7), A057196(2^k+9), this sequence (2^k+11), A102634 (2^k+13), A057197 (2^k+15), A057200 (2^k+17), A057221 (2^k+19), A057201 (2^k+21), A057203 (2^k+23).

Programs

Mathematica

Do[ If[ PrimeQ[2^n + 11], Print[n]], {n, 15250}] (* Robert G. Wilson v, Jan 21 2005 *)

PARI

for(n=1,9e9,ispseudoprime(2^n+11)&&print1(n",")) \\ M. F. Hasler, Jul 18 2016

Extensions

a(18)-a(22) from Robert G. Wilson v, Jan 21 2005

a(23)-a(33) from Robert Price, Dec 06 2013

Edited by M. F. Hasler, Jul 18 2016