A165780 Numbers n such that |2^n-16257| is prime.

2, 3, 6, 8, 10, 12, 14, 16, 20, 22, 26, 30, 34, 36, 38, 43, 44, 50, 58, 64, 68, 80, 116, 142, 146, 254, 296, 298, 306, 396, 456, 730, 876, 1004, 1006, 1051, 1094, 1776, 1896, 1908, 2502, 2876, 3824, 3882, 4796, 4818, 5006, 5704, 6722, 8467, 9676

Offset

1,1

Comments

If p=2^n-16257 is prime, then 2^(n-1)*p is a solution to sigma(x)-2x = 16256 = 2^7*(2^7-1) = 2*A000396(4).

Links

Table of n, a(n) for n=1..51.

Example

a(7)=14 since 2^14-16257 = 127 is prime.
For exponents a(1)=2 through a(6)=12, we get negative values for 2^a(k)-16257, which are prime in absolute value.

Mathematica

Select[Table[{n, Abs[2^n - 16257]}, {n, 0, 100}], PrimeQ[#[[2]]] &][[All, 1]](* G. C. Greubel, Apr 08 2016 *)

Prog

(PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(abs(2^n-16257)), print1(n, ", "))); \\ Altug Alkan, Apr 08 2016
(Magma) [n: n in [1..1100] |IsPrime(2^n-16257)]; // Vincenzo Librandi, Apr 09 2016

Crossrefs

Cf. A096818, A165778, A165779.

Sequence in context: A187750 A089422 A316571 * A051935 A324690 A181486

Adjacent sequences: A165777 A165778 A165779 * A165781 A165782 A165783

Keyword

nonn

Author

M. F. Hasler, Oct 11 2009

Extensions

More terms from Altug Alkan, Apr 08 2016

Status

approved