A057201 Numbers k such that 2^k + 21 is prime.

1, 3, 4, 5, 7, 8, 11, 15, 16, 19, 44, 48, 51, 52, 61, 163, 196, 456, 492, 911, 997, 1616, 1631, 1647, 1803, 1899, 3112, 3584, 3956, 6848, 7023, 9535, 16657, 27035, 33843, 36551, 38859, 81485, 107287, 131383, 139476, 158497, 210061, 216752, 339168, 341355, 376731, 1173095

Offset: 1

Author

Robert G. Wilson v, Sep 16 2000

Keywords

• nonn

Comments

a(48) > 5*10^5. - Robert Price, Sep 17 2015

Examples

			k = 15, 2^15 + 21 = 32789 is prime.
k = 16, 2^16 + 21 = 65557 is prime.
		

Links

• Henri Lifchitz and Renaud Lifchitz, Search for 2^n+21, PRP Top Records.

Crossrefs

Cf. A094076.

Cf. A019434 (primes 2^k+1), A057732 (2^k+3), A059242 (2^k+5), A057195 (2^k+7), A057196 (2^k+9), A102633 (2^k+11), A102634 (2^k+13), A057197 (2^k+15), A057200 (2^k+17), A057221 (2^k+19), this sequence (2^k+21), A057203 (2^k+23).

Programs

Magma

[n: n in [0..1000] | IsPrime(2^n+21)]; // Vincenzo Librandi, Aug 28 2015

Mathematica

Do[ If[ PrimeQ[ 2^n + 21 ], Print[ n ] ], {n, 1, 4000} ]
Select[Range[10000], PrimeQ[2^# + 21] &] (* Vincenzo Librandi, Aug 28 2015 *)

PARI

is(n)=isprime(2^n+21) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(30)-a(47) from Robert Price, Dec 06 2013

a(48) found by Stefano Morozzi, added by Elmo R. Oliveira, Nov 25 2023