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A002254 Numbers k such that 5*2^k + 1 is prime.
(Formerly M2635 N1046)
12

%I M2635 N1046

%S 1,3,7,13,15,25,39,55,75,85,127,1947,3313,4687,5947,13165,23473,26607,

%T 125413,209787,240937,819739,1282755,1320487,1777515

%N Numbers k such that 5*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 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 R. M. Robinson, <a href="/A002253/a002253_1.pdf"> 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. [Annotated scanned copy of selected pages. The first page is (accidentally) included with the scan of the Wilson letter below.]

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

%H R. G. Wilson v, <a href="/A002253/a002253.pdf">Letter (FAX) to N. J. A. Sloane, May 20 1994, concerning A002253-A002274, A000043, A002235-A002240, A001770-A001775, A007117, and many other sequences</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 lst={};Do[If[PrimeQ[5*2^n+1], AppendTo[lst, n]], {n, 0, 2*10^3}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 19 2008 *)

%o (PARI) is(n)=isprime(5*2^n+1) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. A050526.

%K hard,more,nonn

%O 1,2

%A _N. J. A. Sloane_

%E Corrected (removed incorrect term 40937) and added more terms (from http://web.archive.org/web/20161028080239/http://www.prothsearch.net/riesel.html), _Joerg Arndt_, Apr 07 2013

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Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)