A002590 Largest prime factor of 16^n + 1. (Formerly M5046 N2180)

2, 17, 257, 241, 65537, 61681, 673, 15790321, 6700417, 38737, 4278255361, 2931542417, 22253377, 308761441, 54410972897, 4562284561, 67280421310721, 2879347902817, 487824887233, 24517014940753, 44479210368001, 88959882481

Offset

0,1

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. 88.

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..280 (terms 0..256 from Sean A. Irvine, term 277 from Tyler Busby)

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) = A002587(4*n).

Mathematica

Join[{1}, Table[FactorInteger[16^n+1][[-1, 1]], {n, 25}]] (* Harvey P. Dale, Feb 26 2012 *)

Crossrefs

Sequence in context: A020561 A099702 A253549 * A029735 A291206 A037896

Adjacent sequences: A002587 A002588 A002589 * A002591 A002592 A002593

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Don Reble, Nov 14 2006

a(0) corrected by Sean A. Irvine, Apr 20 2014

Status

approved