A117131 Remainder when n^n is divided by the n-th prime number.
1, 1, 2, 4, 1, 12, 12, 7, 2, 6, 24, 26, 11, 6, 30, 15, 9, 41, 39, 32, 51, 64, 78, 4, 72, 43, 89, 25, 31, 109, 26, 62, 80, 36, 9, 72, 132, 140, 105, 52, 132, 135, 117, 147, 79, 193, 93, 49, 175, 76, 64, 187, 196, 9, 163, 221, 190, 62, 102, 280, 71, 87, 102, 268
Offset: 1
Examples
a(8)=7 because 8^8 is 16777216, the 8th prime is 19 and 16777216 modulo 19 is 7.
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000
Programs
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Magma
[Modexp(n, n, NthPrime(n)): n in [1..100]]; // Vincenzo Librandi, Mar 20 2019
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Maple
a:= n-> n&^n mod ithprime(n): seq(a(n), n=1..81); # Alois P. Heinz, Mar 20 2019
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Mathematica
Table[PowerMod[n, n, Prime[n]], {n, 100}] (* T. D. Noe, Aug 20 2013 *) -
PARI
a(n) = lift(Mod(n, prime(n))^n); \\ Michel Marcus, Mar 20 2019
Formula
a(n) = mod(n^n, prime(n)).
Extensions
More terms from Franklin T. Adams-Watters, Jul 26 2006