A110146 a(n) = n^(n+1) mod (n+2).

0, 1, 0, 1, 4, 1, 0, 4, 8, 1, 4, 1, 12, 4, 0, 1, 4, 1, 12, 4, 20, 1, 16, 16, 24, 13, 20, 1, 28, 1, 0, 4, 32, 9, 4, 1, 36, 4, 32, 1, 10, 1, 36, 31, 44, 1, 16, 15, 38, 4, 44, 1, 40, 49, 40, 4, 56, 1, 52, 1, 60, 4, 0, 16, 34, 1, 60, 4, 48, 1, 40, 1, 72, 34, 68, 9

Offset: 0

Author

Zak Seidov, Jul 14 2005

Keywords

• nonn

Comments

First occurrence of n such that n^(n+1) (mod n+2) == k for k = 1, 2, 3, ..., or 0 if no such n is known: 1, 20735, 10667, 4, 0, 3761, 3820819, 8, 33, 40, 350849481, 12, 25, ..., .

Congruences not yet occurring for n < 4.6*10^9: 5, 47, 57, 105, 203, 233, 255, 293, 333, 354, 377, 405, 433, ..., .

Links

• Carl R. White, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000918, A040976.

Programs

Mathematica

Table[PowerMod[n, n+1, n+2], {n, 0, 120}]

PARI

a(n) = lift(Mod(n, n+2)^(n+1)); \\ Michel Marcus, Dec 17 2022

Formula

a(A000918(n)) = 0 for n >= 1, a(A040976(n)) = 1 for n >= 2.

a(n-2) = A062173(n) if n is odd or n is power of two, and a(n-2) = n - A062173(n) otherwise. - Thomas Ordowski, Nov 28 2013