A271234 2^(p-1) modulo p^3, where p = prime(n).

2, 4, 16, 64, 1024, 1899, 1667, 1502, 8856, 10122, 14602, 20573, 27840, 10321, 92638, 86179, 35283, 54291, 126363, 211865, 313171, 338516, 114209, 317375, 598297, 702961, 822971, 1089047, 684521, 928748, 421641, 911761, 739253, 912258, 2634023, 829293, 505855

Offset

1,1

Comments

H. S. Vandiver showed that a(n) = 1 if and only if sum{k=1, p-2}(1/k) == 0 (mod p^2), where k runs over the odd numbers up to p-2 (cf. Dickson, 1917, p. 187).

Clearly, if a(n) = 1, then p is a Wieferich prime, i.e., a term of A001220.

Links

Felix Fröhlich, Table of n, a(n) for n = 1..10000

L. E. Dickson, Fermat's Last Theorem and the Origin and Nature of the Theory of Algebraic Numbers, Annals of Mathematics, Second Series, Vol. 18, No. 4 (1917), 161-187.

Prog

(PARI) a(n) = my(p=prime(n)); lift(Mod(2, p^3)^(p-1))

Crossrefs

Cf. A001220, A196202.

Sequence in context: A154004 A338364 A060656 * A061286 A288756 A019279

Adjacent sequences: A271231 A271232 A271233 * A271235 A271236 A271237

Keyword

nonn

Author

Felix Fröhlich, Apr 02 2016

Status

approved