A110146 - OEIS

%I #32 Dec 17 2022 12:41:27

%S 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,

%T 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,

%U 1,52,1,60,4,0,16,34,1,60,4,48,1,40,1,72,34,68,9

%N a(n) = n^(n+1) mod n+2.

%C 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, ..., .

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

%H Carl R. White, <a href="/A110146/b110146.txt">Table of n, a(n) for n = 0..10000</a>

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

%F 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

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

%o (PARI) a(n) = lift(Mod(n, n+2)^(n+1)); \\ _Michel Marcus_, Dec 17 2022

%Y Cf. A000918, A040976.

%K nonn

%O 0,5

%A _Zak Seidov_, Jul 14 2005