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

0,5

Comments

First occurrence of n such that n^(n+1) (modulo 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, ..., .

Congruencies 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

Formula

a(A000918)==0, a(A040976)==1.

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000918, A040976.

Sequence in context: A021713 A122388 A094918 * A126217 A303499 A108944

Adjacent sequences: A110143 A110144 A110145 * A110147 A110148 A110149

Keyword

nonn

Author

Zak Seidov, Jul 14 2005

Status

approved