A374964 a(n) is the smallest positive k such that -n^n == n (mod n + k).

1, 1, 2, 1, 5, 1, 3, 1, 9, 1, 11, 1, 13, 1, 14, 1, 17, 1, 7, 1, 21, 1, 23, 1, 25, 1, 3, 1, 29, 1, 6, 1, 33, 1, 35, 1, 37, 1, 39, 1, 41, 1, 7, 1, 45, 1, 18, 1, 49, 1, 50, 1, 53, 1, 19, 1, 45, 1, 59, 1, 61, 1, 7, 1, 65, 1, 63, 1, 44, 1, 71, 1, 40, 1, 12, 1, 12, 1, 27, 1, 81, 1, 23, 1, 85, 1, 58, 1, 8, 1, 6, 1, 9

Offset

1,3

Links

Table of n, a(n) for n=1..93.

Formula

a(n) = 1 for n even and a(n) <= n for n odd. - Michael S. Branicky, Jul 28 2024

a(n) + n is the least divisor > n of n^n + n. - Robert Israel, Jul 30 2024

Maple

f:= proc(n) local k;
  for k from 1 do if n &^ n + n mod (n+k) = 0 then return k fi od
end proc:
map(f, [$1..100]); # Robert Israel, Jul 30 2024

Mathematica

a[n_] := Module[{k = 1}, While[PowerMod[n, n, n + k] != k, k++]; k]; Array[a, 100] (* Amiram Eldar, Jul 26 2024 *)

Prog

(Python)
def a(n): return next(k for k in range(1, n+1) if pow(n, n, n+k) == k)
print([a(n) for n in range(1, 94)]) # Michael S. Branicky, Jul 26 2024
(Python)
from itertools import count
def A374964(n):
    m = n**n+n
    return next(d for d in count(1) if not m%(n+d)) # Chai Wah Wu, Aug 12 2024
(PARI) a(n) = my(k=1); while (-Mod(n, n+k)^n != n, k++); k; \\ Michel Marcus, Jul 26 2024

Crossrefs

Cf. A066068 (n^n+n).

Sequence in context: A378783 A055972 A342414 * A079168 A332085 A055205

Adjacent sequences: A374961 A374962 A374963 * A374965 A374966 A374967

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 25 2024

Status

approved