A002589 Largest primitive factor of 2^(2n+1) + 1. (Formerly M2234 N0886)

3, 1, 11, 43, 19, 683, 2731, 331, 43691, 174763, 5419, 2796203, 4051, 87211, 3033169, 715827883, 20857, 86171, 25781083, 22366891, 8831418697, 2932031007403, 18837001, 165768537521, 4363953127297, 6529, 28059810762433, 48912491, 160465489

Offset

0,1

Comments

Also excludes intrinsic factors which is why a(1)=1 rather than 3. - Sean A. Irvine, Apr 20 2014

References

J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.

M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 2, p. 85.

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

Table of n, a(n) for n = 0..560

J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

Sequence in context: A362996 A153257 A002185 * A048522 A365035 A232460

Adjacent sequences: A002586 A002587 A002588 * A002590 A002591 A002592

Keyword

nonn

Author

N. J. A. Sloane

Extensions

a(22)-a(472) from Sean A. Irvine, Apr 20 2014

a(473)-a(560) from Max Alekseyev, Feb 09 2020, Sep 10 2020, Dec 21 2022, Jul 25 2023

Status

approved