A067462 a(n) = (1! + 2! + ... + (n-1)!) mod n.

0, 1, 0, 1, 3, 3, 5, 1, 0, 3, 0, 9, 9, 5, 3, 9, 12, 9, 8, 13, 12, 11, 20, 9, 13, 9, 9, 5, 16, 3, 1, 25, 0, 29, 33, 9, 4, 27, 9, 33, 3, 33, 15, 33, 18, 43, 17, 9, 47, 13, 12, 9, 12, 9, 33, 33, 27, 45, 27, 33, 21, 1, 54, 25, 48, 33, 64, 29, 66, 33, 67, 9, 54, 41, 63, 65, 33, 9, 19, 73, 63

Offset: 1

Author

Alex Fink, Feb 24 2002

Keywords

• easy
• nonn

Links

• A.H.M. Smeets, Table of n, a(n) for n = 1..20000 (first 1000 terms from T. D. Noe)

Crossrefs

Cf. A049782.

Programs

Mathematica

Mod[ #[[1]], #[[2]]]&/@Transpose[{Rest[FoldList[Plus, 0, Factorial[Range[90]]]], Range[90]}]
Table[Mod[Total[Range[n-1]!],n],{n,90}] (* Harvey P. Dale, Jan 23 2023 *)

PARI

a(n) = my(s=0, p=1); for (i=1, n-1, f = Mod(i, n); p*=f; s += p); lift(s); \\ Michel Marcus, Aug 19 2019

Python

n = 0
while n < 200:
    n,f,fs,i = n+1,1,0,1
    while i < n:
        f,i = (f*i)%n,i+1
        fs = (fs+f)%n
    print(n,fs) # A.H.M. Smeets, Aug 19 2019