A002184 a(n) = least primitive factor of 2^(2n+1) - 1.

1, 7, 31, 127, 73, 23, 8191, 151, 131071, 524287, 337, 47, 601, 262657, 233, 2147483647, 599479, 71, 223, 79, 13367, 431, 631, 2351, 4432676798593, 103, 6361, 881, 32377, 179951, 2305843009213693951, 92737, 145295143558111, 193707721, 10052678938039, 228479, 439, 100801, 581283643249112959, 2687, 2593, 167

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

For n > 0, 2^(a(n)-2n-2) == 1 (mod a(n)), since 2^(a(n)-1) == 2^(2n+1) == 1 (mod a(n)). - Thomas Ordowski, Aug 11 2021

a(n) == 1 (mod 2n+1). - Thomas Ordowski, Aug 11 2021

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. 84.
• 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..602
• 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

Cf. A002588, A112927.

Formula

a(n) = A112927(2n+1). - Max Alekseyev, Apr 26 2022

Extensions

More terms from Don Reble, Nov 14 2006