A002236 Numbers k such that 9*2^k - 1 is prime.
1, 3, 7, 13, 15, 21, 43, 63, 99, 109, 159, 211, 309, 343, 415, 469, 781, 871, 939, 1551, 3115, 3349, 5589, 5815, 5893, 7939, 8007, 11547, 12495, 22555, 23647, 35647, 83415, 103059, 184999, 275859, 384243, 484975, 503893, 828709, 1010277, 1419855, 1481821
Offset: 1
References
- H. Riesel, "Prime numbers and computer methods for factorization," Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, see pp. 381-384.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Jeppe Stig Nielsen, Table of n, a(n) for n = 1..48
- Wilfrid Keller, List of primes k.2^n - 1 for k < 300
- C. K. Caldwell, The Prime Pages
- The Prime Pages, Search output for 9*2^k - 1
- Prime-Wiki, Riesel primes of the form 9*2^n - 1
- Kosmaj, Riesel list k<300.
- H. Riesel, Lucasian criteria for the primality of N=h.2^n-1, Math. Comp., 23 (1969), 869-875.
- Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime
Crossrefs
Cf. A050524.
Programs
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Mathematica
b=9; i=0; Table[While[i++; cp=b*2^i-1; !PrimeQ[cp]]; i, {j, 1, 22}] (* Lei Zhou, Nov 08 2013 *) 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 *) -
PARI
is(n)=ispseudoprime(9*2^n-1) \\ Charles R Greathouse IV, Feb 17 2017
Extensions
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
a(42)-a(43) communicated by Jeppe Stig Nielsen, Jun 08 2023
Comments