OFFSET
1,1
COMMENTS
a(n) = 2 if and only if n == {0, 1} (mod 4).
a(n) <= A151800(n).
The sequence is unbounded.
Numbers n such that a(n-1) = n are 2, 3, 7, 23, 31, 43, 59, 139, 283, ...
By the Agoh-Giuga conjecture, if a(n-1) = n, then n is a prime.
It seems that if a(n) > n, then a(n) is a prime (the next prime after n).
If a(n) = n, then n is in A121707. These numbers are 35, 143, 187, 215, ...
Conjecture: all composite terms of the sequence are A121707.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..1000 from Seiichi Manyama)
Wikipedia, Agoh-Giuga conjecture
MATHEMATICA
a[n_] := Block[{k=2}, While[Mod[Sum[PowerMod[j, k-1, k], {j, n}], k] != Mod[n, k], k++]; k]; Array[a, 81] (* Giovanni Resta, Jul 29 2018 *)
PROG
(PARI) a(n) = for(k=2, oo, if (sum(j=1, n, Mod(j, k)^(k-1)) == n, return (k)); ); \\ Michel Marcus, Jul 26 2018
(Python)
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 A317358(n):
k = 2
while g(n, k-1, k):
k += 1
return k # Chai Wah Wu, Jul 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ordowski, Jul 26 2018
EXTENSIONS
More terms from Michel Marcus, Jul 26 2018
STATUS
approved