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A268000 p*B_(p-1)+1 modulo p^2, where p = prime(n) and B_i denotes the i-th Bernoulli number. 1
0, 6, 5, 42, 22, 13, 102, 57, 207, 551, 620, 296, 697, 602, 329, 1855, 1652, 3477, 871, 4970, 876, 5846, 1743, 6319, 6887, 7373, 5974, 214, 3379, 10848, 9144, 15720, 7809, 9452, 14155, 13137, 23864, 17767, 3674, 18511, 8771, 13213, 30560, 6948, 29156, 23681 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Related to the Agoh-Giuga conjecture (called Agoh's conjecture by Borwein, Borwein, Borwein and Girgensohn) which states that a positive integer k is prime if and only if k*B_(k-1) == -1 (mod k) (see Wikipedia and Borwein, Borwein, Borwein, Girgensohn, 1996, open problem 10).

Up to p = 101839, there are only two primes p such that a(n) = 0, namely 2 and 1277, i.e., a(1) = 0 and a(206) = 0. Do any other such primes exist?

LINKS

Felix Fröhlich, Table of n, a(n) for n = 1..1000

D. Borwein, J. M. Borwein, P. B. Borwein and R. Girgensohn, Giuga's conjecture on primality, The American Mathematical Monthly, Vol. 103, No. 1 (1996), 40-50.

Wikipedia, Agoh-Giuga conjecture

PROG

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

CROSSREFS

Sequence in context: A288211 A038259 A302750 * A223529 A189422 A266980

Adjacent sequences:  A267997 A267998 A267999 * A268001 A268002 A268003

KEYWORD

nonn

AUTHOR

Felix Fröhlich, Jan 24 2016

STATUS

approved

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Last modified April 7 01:11 EDT 2020. Contains 333291 sequences. (Running on oeis4.)