A258818 - OEIS

%I #9 Sep 12 2017 10:00:08

%S 1,2,3,0,4,9,13,4,14,25,4,30,4,9,32,30,45,48,12,7,34,74,40,76,96,57,

%T 64,90,89,50,117,87,29,46,108,113,10,70,111,150,14,153,119,26,81,78,

%U 112,209,173,177,186,126,26,25,60,74,23,27,138,49,72,211,252,169

%N a(n) = (!0 + !1 + ... + !(p-1)) mod p, where p = prime(n).

%C !n is a subfactorial number (A000166).

%C This is A173184(p) mod p where p = prime(n) .

%H Michel Lagneau, <a href="/A258818/b258818.txt">Table of n, a(n) for n = 1..1000</a>

%e For n=3, prime(3) = 5 => !0 + !1 + !2 + !3 + !4 = 1 + 0 + 1 + 2 + 9 = 13 == 3 (mod 5), so a(3) = 3.

%p A:= proc(n) option remember; if n<=1 then 1-n else (n-1)*(procname(n-1)+procname(n-2)); fi; end;

%p a:=n->n!*sum((-1)^k/k!, k=0..n):

%p lf:=n->add(A(k), k=0..n-1); [seq(lf(ithprime(n)) mod ithprime(n), n=1..40)];

%t Table[Mod[Total[Subfactorial[Range[0, n-1]]], n], {n, Prime[Range[70]]}]

%Y Cf. A258817.

%K nonn

%O 1,2

%A _Michel Lagneau_, Jun 11 2015