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A002256 Numbers k such that 9*2^k + 1 is prime.
(Formerly M0751 N0283)
4

%I M0751 N0283 #45 Jan 27 2023 11:39:58

%S 1,2,3,6,7,11,14,17,33,42,43,63,65,67,81,134,162,206,211,366,663,782,

%T 1305,1411,1494,2297,2826,3230,3354,3417,3690,4842,5802,6937,7967,

%U 9431,13903,22603,24422,39186,43963,47003,49902,67943,114854,127003,145247

%N Numbers k such that 9*2^k + 1 is prime.

%D H. Riesel, "Prime numbers and computer methods for factorization", Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, see pp. 381-384.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Jeppe Stig Nielsen, <a href="/A002256/b002256.txt">Table of n, a(n) for n = 1..60</a>

%H Ray Ballinger, <a href="http://www.prothsearch.com/index.html">Proth Search Page</a>

%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 C. K. Caldwell, <a href="http://www.utm.edu/research/primes/">The Prime Pages</a>

%H Y. Gallot, <a href="http://www.utm.edu/research/primes/programs/gallot/index.html">Proth.exe: Windows Program for Finding Large Primes</a>

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

%H R. M. Robinson, <a href="https://doi.org/10.1090/S0002-9939-1958-0096614-7">A report on primes of the form k.2^n+1 and on factors of Fermat numbers</a>, Proc. Amer. Math. Soc., 9 (1958), 673-681.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ProthPrime.html">Proth Prime</a>

%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 Select[Range[2019],PrimeQ[9*2^#+1]&] (* _Metin Sariyar_, Sep 21 2019 *)

%Y Cf. A050528.

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E a(48) from _Arkadiusz Wesolowski_, Oct 22 2011

%E Added more terms (from http://web.archive.org/web/20161028080239/http://www.prothsearch.net/riesel.html), _Joerg Arndt_, Apr 07 2013

%E Terms moved from Data to b-file, and more terms put in b-file, by _Jeppe Stig Nielsen_, Sep 21 2019

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Last modified July 17 10:44 EDT 2024. Contains 374377 sequences. (Running on oeis4.)