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A002236 Numbers k such that 9*2^k - 1 is prime.

%I A002236 M2634 N1045 #48 Jun 24 2023 07:48:09
%S A002236 1,3,7,13,15,21,43,63,99,109,159,211,309,343,415,469,781,871,939,1551,
%T A002236 3115,3349,5589,5815,5893,7939,8007,11547,12495,22555,23647,35647,
%U A002236 83415,103059,184999,275859,384243,484975,503893,828709,1010277,1419855,1481821
%N A002236 Numbers k such that 9*2^k - 1 is prime.
%C A002236 Even exponents can give at most semiprimes (see A181490). - _Jeppe Stig Nielsen_, Jun 08 2023
%D A002236 H. Riesel, "Prime numbers and computer methods for factorization," Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, see pp. 381-384.
%D A002236 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002236 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002236 Jeppe Stig Nielsen, <a href="/A002236/b002236.txt">Table of n, a(n) for n = 1..48</a>
%H A002236 Wilfrid Keller, <a href="http://www.prothsearch.com/riesel2.html">List of primes k.2^n - 1 for k < 300</a>
%H A002236 C. K. Caldwell, <a href="https://t5k.org/research/primes/">The Prime Pages</a>
%H A002236 The Prime Pages, <a href="https://t5k.org/primes/search.php?Description=%5E9*2%5E%25-1%24&amp;OnList=all&amp;Number=200&amp;Style=HTML">Search output for 9*2^k - 1</a>
%H A002236 Prime-Wiki, <a href="https://www.rieselprime.de/ziki/Riesel_prime_2_9">Riesel primes of the form 9*2^n - 1</a>
%H A002236 Kosmaj, <a href="https://web.archive.org/web/20210503224738/http://www.15k.org/riesellist.html">Riesel list k<300</a>.
%H A002236 H. Riesel, <a href="http://dx.doi.org/10.1090/S0025-5718-1969-0262163-1">Lucasian criteria for the primality of N=h.2^n-1</a>, Math. Comp., 23 (1969), 869-875.
%H A002236 <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 A002236 b=9; i=0; Table[While[i++; cp=b*2^i-1; !PrimeQ[cp]]; i, {j, 1, 22}] (* _Lei Zhou_, Nov 08 2013 *)
%t A002236 Select[Range[3400],PrimeQ[9*2^#-1]&] (* The program generates the first 22 terms of the sequence. To generate more, increase the Range constant, but the program may take a long time to run. *) (* _Harvey P. Dale_, Sep 01 2020 *)
%o A002236 (PARI) is(n)=ispseudoprime(9*2^n-1) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y A002236 Cf. A050524.
%K A002236 hard,nonn,nice
%O A002236 1,2
%A A002236 _N. J. A. Sloane_
%E A002236 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
%E A002236 a(42)-a(43) communicated by _Jeppe Stig Nielsen_, Jun 08 2023