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

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%I A110146 #38 May 07 2025 11:27:05
%S A110146 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 A110146 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 A110146 1,52,1,60,4,0,16,34,1,60,4,48,1,40,1,72,34,68,9
%N A110146 a(n) = n^(n+1) mod (n+2).
%C A110146 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, ..., .
%C A110146 Congruences not yet occurring for n < 4.6*10^9: 5, 47, 57, 105, 203, 233, 255, 293, 333, 354, 377, 405, 433, ..., .
%H A110146 Carl R. White, <a href="/A110146/b110146.txt">Table of n, a(n) for n = 0..10000</a>
%F A110146 a(A000918(n)) = 0 for n >= 1, a(A040976(n)) = 1 for n >= 2.
%F A110146 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 A110146 Table[PowerMod[n, n+1, n+2], {n, 0, 120}]
%o A110146 (PARI) a(n) = lift(Mod(n, n+2)^(n+1)); \\ _Michel Marcus_, Dec 17 2022
%Y A110146 Cf. A000918, A040976.
%K A110146 nonn
%O A110146 0,5
%A A110146 _Zak Seidov_, Jul 14 2005