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

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

Author

N. J. A. Sloane

Keywords

• nonn

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

• Max Alekseyev, Table of n, a(n) for n = 0..563
• 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

Extensions

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

a(473)-a(563) from Max Alekseyev, Feb 09 2020 - Feb 25 2024