A050539 Numbers k such that 27*2^k-1 is prime.

1, 2, 4, 5, 8, 10, 14, 28, 37, 38, 70, 121, 122, 160, 170, 253, 329, 362, 454, 485, 500, 574, 892, 962, 1213, 1580, 2642, 2708, 4505, 8152, 11858, 13300, 15041, 16118, 16778, 19069, 22769, 29020, 30298, 30377, 35942, 42817, 42869, 62024, 74629, 90449, 91042, 117901, 128594, 143330, 152530, 157898, 175852, 340682, 444622, 627794, 729314, 777992, 1108214, 1163629, 1253870

Offset: 1

Author

N. J. A. Sloane, Dec 29 1999

Keywords

• hard
• nonn

Comments

3855094, 4542344 and 4583717 are also in the sequence. - Felix Fröhlich, Sep 19 2014

Links

• Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for k < 300
• Wilfrid Keller, List of primes k.2^n - 1 for k < 300
• Kosmaj, Riesel list k<300.
• PrimeGrid, Announcement of n=3855094 , Announcement of n=4542344, Announcement of n=4583717 - _Felix Fröhlich_, Sep 19 2014
• Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Crossrefs

Cf. A032363 = 27*2^n+1 is prime.

Programs

Mathematica

For[n = 1, n <= 10000, n++, If[PrimeQ[27*2^n - 1], Print[n]]] (* Wesley Ivan Hurt, May 19 2014 *)
Select[Range[1000], PrimeQ[27*2^# - 1] & ] (* Robert Price, Dec 22 2018 *)

PARI

a(n)=if(ispseudoprime(27*2^n-1), print1(n, ", ")) \\ Felix Fröhlich, Sep 19 2014

Extensions

More terms from Hugo Pfoertner, Aug 17 2004

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(59)-a(61) from the Wilfrid Keller link by Robert Price, Dec 22 2018