A002184 a(n) = least primitive factor of 2^(2n+1) - 1. (Formerly M4400 N1855)

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

0,2

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

Formula

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

Crossrefs

Cf. A002588, A112927.

Sequence in context: A181951 A218963 A125193 * A002588 A327497 A036280

Adjacent sequences: A002181 A002182 A002183 * A002185 A002186 A002187

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Don Reble, Nov 14 2006

Status

approved