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A317357 a(n) is the smallest composite k > n such that 1^(k-1) + 2^(k-1) + ... + n^(k-1) == n (mod k). 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 24 11:56 EST 2021. Contains 341569 sequences. (Running on oeis4.)