A057197 Numbers k such that 2^k + 15 is prime.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 22, 23, 26, 30, 32, 40, 42, 46, 61, 72, 76, 155, 180, 198, 203, 310, 328, 342, 508, 510, 515, 546, 808, 1563, 2772, 3882, 3940, 4840, 7518, 11118, 11552, 11733, 12738, 12858, 17421, 44122, 64660, 163560, 172455, 180496, 325866, 481840, 1009168

Offset: 1

Author

Robert G. Wilson v, Sep 15 2000

Keywords

• nonn

Comments

a(55) > 5*10^5. - Robert Price, Sep 14 2015

For these numbers k, 2^(k-1)*(2^k+15) has deficiency 16 (see A125248). - M. F. Hasler, Jul 18 2016

Examples

			For k = 5, 2^5 + 15 = 47 is prime.
For k = 15, 2^15 + 15 = 32783 is prime.
		

Links

• Henri Lifchitz and Renaud Lifchitz (Editors), Search for 2^n+15, PRP Top Records.

Crossrefs

Cf. A094076, A125248.

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), this sequence (2^k+15), A057200 (2^k+17), A057221 (2^k+19), A057201 (2^k+21), A057203 (2^k+23).

Programs

Magma

[n: n in [0..1500] | IsPrime(2^n+15)]; // Vincenzo Librandi, Aug 28 2015

Mathematica

Do[ If[ PrimeQ[ 2^n + 15 ], Print[n]], { n, 1, 12422 }]
Select[Range[15000], PrimeQ[2^# + 15] &] (* Vincenzo Librandi, Aug 28 2015 *)

PARI

for(n=1,oo,ispseudoprime(2^n+15)&&print1(n",")) \\ M. F. Hasler, Jul 18 2016

Extensions

a(45)-a(53) from Robert Price, Dec 06 2013

a(54) from Robert Price, Sep 14 2015

a(55) from Stefano Morozzi, added by Elmo R. Oliveira, Dec 11 2023