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

1,5

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A049782.

Sequence in context: A371659 A246005 A103786 * A320298 A021753 A353412

Adjacent sequences: A067459 A067460 A067461 * A067463 A067464 A067465

Keyword

easy,nonn

Author

Alex Fink, Feb 24 2002

Status

approved