login
Numbers k such that 27*2^k-1 is prime.
5

%I #35 Jan 17 2019 10:08:17

%S 1,2,4,5,8,10,14,28,37,38,70,121,122,160,170,253,329,362,454,485,500,

%T 574,892,962,1213,1580,2642,2708,4505,8152,11858,13300,15041,16118,

%U 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

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

%C 3855094, 4542344 and 4583717 are also in the sequence. - _Felix Fröhlich_, Sep 19 2014

%H Ray Ballinger and Wilfrid Keller, <a href="http://www.prothsearch.com/riesel1.html">List of primes k.2^n + 1 for k < 300</a>

%H Wilfrid Keller, <a href="http://www.prothsearch.com/riesel2.html">List of primes k.2^n - 1 for k < 300</a>

%H Kosmaj, <a href="http://www.15k.org/riesellist.html">Riesel list k<300</a>.

%H PrimeGrid, <a href="http://www.primegrid.com/download/27121-3855094.pdf">Announcement of n=3855094</a> , <a href="http://www.primegrid.com/download/27121-4542344.pdf">Announcement of n=4542344</a>, <a href="http://www.primegrid.com/download/27121-4583717.pdf">Announcement of n=4583717</a> - _Felix Fröhlich_, Sep 19 2014

%H <a href="/index/Pri#riesel">Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime</a>

%t For[n = 1, n <= 10000, n++, If[PrimeQ[27*2^n - 1], Print[n]]] (* _Wesley Ivan Hurt_, May 19 2014 *)

%t Select[Range[1000], PrimeQ[27*2^# - 1] & ] (* _Robert Price_, Dec 22 2018 *)

%o (PARI) a(n)=if(ispseudoprime(27*2^n-1), print1(n, ", ")) \\ _Felix Fröhlich_, Sep 19 2014

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

%K hard,nonn

%O 1,2

%A _N. J. A. Sloane_, Dec 29 1999

%E More terms from _Hugo Pfoertner_, Aug 17 2004

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

%E a(59)-a(61) from the Wilfrid Keller link by _Robert Price_, Dec 22 2018