A002235 Numbers m such that 3*2^m - 1 is prime. (Formerly M0545 N0195)

0, 1, 2, 3, 4, 6, 7, 11, 18, 34, 38, 43, 55, 64, 76, 94, 103, 143, 206, 216, 306, 324, 391, 458, 470, 827, 1274, 3276, 4204, 5134, 7559, 12676, 14898, 18123, 18819, 25690, 26459, 41628, 51387, 71783, 80330, 85687, 88171, 97063, 123630, 155930, 164987, 234760

Offset

1,3

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..64

C. K. Caldwell, The Prime Pages: Database Search Output

Wilfrid Keller, List of primes k.2^n - 1 for k < 300

Mersenne Forum, 321 Search

H. Riesel, Lucasian criteria for the primality of N=h.2^n-1, Math. Comp., 23 (1969), 869-875.

H. Riesel, Lucasian criteria for the primality of N=h.2^n-1, Math. Comp., 23 (1969), 869-875. [Annotated scanned copy]

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Eric Weisstein's World of Mathematics, Thabit ibn Kurrah Prime

Eric Weisstein's World of Mathematics, Thabit ibn Kurrah Rule

Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Mathematica

lst={}; Do[If[PrimeQ[3*2^n-1], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)

Prog

(PARI) is(n)=ispseudoprime(3<<n - 1) \\ Charles R Greathouse IV, Aug 27 2014

Crossrefs

Cf. A000043, A007505, A003307, A046865, A079906, A046866, A001771, A005541, A056725, A046867, A079907.

Sequence in context: A215231 A301512 A091336 * A217132 A239014 A030705

Adjacent sequences: A002232 A002233 A002234 * A002236 A002237 A002238

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from Eric W. Weisstein, Sep 29 2007

a(60) = 11484018 from The Prime Pages, from Pierre CAMI, Nov 25 2014

a(61)-a(62) from The Prime Pages, from Eric W. Weisstein, Nov 03 2015

Terms moved from Data to b-file, and more terms added to b-file, by Jeppe Stig Nielsen, Sep 07 2021

Status

approved