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A002236 Numbers k such that 9*2^k - 1 is prime.
(Formerly M2634 N1045)
9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Even exponents can give at most semiprimes (see A181490). - Jeppe Stig Nielsen, Jun 08 2023
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
C. K. Caldwell, The Prime Pages
H. Riesel, Lucasian criteria for the primality of N=h.2^n-1, Math. Comp., 23 (1969), 869-875.
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 *)
PROG
(PARI) is(n)=ispseudoprime(9*2^n-1) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A050524.
Sequence in context: A092734 A209839 A192854 * A255682 A080565 A164344
KEYWORD
hard,nonn,nice
AUTHOR
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
STATUS
approved

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Last modified July 15 10:24 EDT 2024. Contains 374332 sequences. (Running on oeis4.)