A317357 a(n) is the smallest composite k > n such that 1^(k-1) + 2^(k-1) + ... + n^(k-1) == n (mod k).

4, 341, 473, 6, 10, 133, 497, 14, 12, 15, 15, 16, 18, 143, 35, 20, 32, 51, 57, 38, 28, 77, 253, 36, 30, 65, 39, 36, 58, 115, 155, 62, 36, 187, 119, 40, 74, 57, 247, 52, 80, 287, 2051, 86, 55, 69, 69, 94, 54, 175, 85, 65, 65, 159, 69, 70, 64, 551, 1711, 72

Offset

1,1

Comments

According to the Agoh-Giuga conjecture, a(n) > n+1.

a(n) > A151800(n) for all n < 33.

a(n) <= A271221(n) for n > 1.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..9661

Wikipedia, Agoh-Giuga conjecture

Mathematica

a[n_] := Block[{k = n+1}, While[PrimeQ[k] || Mod[Sum[PowerMod[j, k-1, k], {j, n}], k] != n, k++]; k]; Array[a, 60] (* Giovanni Resta, Jul 26 2018 *)

Prog

(PARI) a(n) = forcomposite(k=n+1, , if (sum(j=1, n, Mod(j, k)^(k-1)) == n, return (k)); ); \\ Michel Marcus, Jul 26 2018
(Python)
from sympy import isprime
def g(n, p, q): # compute (-n + sum_{k=1, n} k^p)  mod q
    c = (-n) % q
    for k in range(1, n+1):
        c = (c+pow(k, p, q)) % q
    return c
def A317357(n):
    k = n+1
    while isprime(k) or g(n, k-1, k):
        k += 1
    return k # Chai Wah Wu, Jul 31 2018

Crossrefs

Cf. A151800, A271221, A317058, A317358.

Sequence in context: A000783 A098654 A317058 * A069884 A332134 A283101

Adjacent sequences: A317354 A317355 A317356 * A317358 A317359 A317360

Keyword

nonn

Author

Thomas Ordowski, Jul 26 2018

Extensions

More terms from Giovanni Resta, Jul 26 2018

Status

approved