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A013584 Smallest m such that 0!+1!+...+(m-1)! is divisible by n, or 0 if no such m exists. 4
1, 2, 0, 3, 4, 0, 6, 0, 0, 4, 6, 0, 0, 6, 0, 0, 5, 0, 7, 0, 0, 6, 7, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 5, 0, 0, 22, 7, 0, 0, 16, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 55, 12, 0, 0, 0, 0, 0, 0, 0, 0, 54, 0, 42, 22, 0, 0, 6, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From Robert Israel, Nov 14 2016: (Start)

a(n) < n for n > 2.

If a(n) = 0, then a(mn) = 0 for all m>=2. (End)

REFERENCES

M. R. Mudge, Smarandache Notions Journal, University of Craiova, Vol. VII, No. 1, 1996.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

f:= proc(n) local t, r, m;

  r:= 1; t:= 1;

  for m from 1 do

    r:= r*m mod n;

    if r = 0 then return 0 fi;

    t:= t + r mod n;

    if t = 0 then return m+1 fi;

  od;

end proc:

f(1):= 1:

map(f, [$1..100]); # Robert Israel, Nov 14 2016

MATHEMATICA

a[n_] := Module[{t, r, m}, r = 1; t = 1; For[m = 1, True, m++, r = Mod[r*m, n]; If[r == 0, Return[0]]; t = Mod[t+r, n]; If[t == 0, Return[m+1]]]];

Array[a, 100] (* Jean-Fran├žois Alcover, Apr 12 2019, after Robert Israel *)

CROSSREFS

Cf. A003422, A013585, A049044, A049045, A275608.

Sequence in context: A117909 A261094 A091538 * A307320 A137372 A212844

Adjacent sequences:  A013581 A013582 A013583 * A013585 A013586 A013587

KEYWORD

nonn

AUTHOR

Michael R. Mudge (Amsorg(AT)aol.com)

STATUS

approved

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Last modified February 16 15:17 EST 2020. Contains 331961 sequences. (Running on oeis4.)