cp's OEIS Frontend

A086330 a(n) = Sum_{m >= 2} m! mod n.

%I A086330 #22 Apr 16 2024 16:52:55
%S A086330 0,2,4,7,2,18,8,17,12,43,8,73,32,17,24,113,26,159,12,32,76,203,8,112,
%T A086330 164,89,60,334,32,496,88,164,232,67,44,706,292,164,32,863,74,874,164,
%U A086330 62,456,1097,56,291,162,317,268,1124,116,142,88,425,566,1560,32,2033,930
%N A086330 a(n) = Sum_{m >= 2} m! mod n.
%C A086330 A discrete infinite sum that has some rough analogies to the infinite series for exponentials.
%F A086330 a(n) = -1 + Sum_{k=1..n} A062169(n, k). - _Vladeta Jovovic_, Sep 06 2003
%e A086330 a(7) = 2! mod 7 + 3! mod 7 + 4! mod 7 + 5! mod 7 + 6! mod 7 + 7! mod 7 + 8! mod 7 + . . . = 2 mod 7 + 6 mod 7 + 24 mod 7 + 120 mod 7 + 720 mod 7 + 5040 mod 7 + 40320 mod 7 + ... = 2 + 6 + 3 + 1 + 6 + (all further values are zero) = 18.
%o A086330 (PARI) a(n) = sum(m=2, n, m! % n) \\ _Michel Marcus_, Jul 23 2013
%o A086330 (Python)
%o A086330 def A086330(n):
%o A086330     a, c = 0, 1
%o A086330     for m in range(2,n):
%o A086330         c = c*m%n
%o A086330         if c==0:
%o A086330             break
%o A086330         a += c
%o A086330     return a # _Chai Wah Wu_, Apr 16 2024
%Y A086330 Cf. A062169.
%K A086330 easy,nonn
%O A086330 2,2
%A A086330 _Walter Carlini_, Aug 31 2003
%E A086330 Corrected and extended by _Vladeta Jovovic_, Sep 06 2003