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A013585 Smallest m such that 1!+...+m! is divisible by 2n+1, or 0 if no such m exists. 2
1, 2, 0, 0, 3, 4, 0, 0, 5, 0, 0, 12, 0, 7, 19, 0, 4, 0, 24, 0, 32, 19, 0, 0, 0, 5, 20, 0, 0, 0, 0, 0, 0, 20, 12, 0, 7, 0, 0, 57, 7, 0, 0, 19, 0, 0, 0, 0, 6, 8, 83, 0, 0, 15, 33, 24, 0, 0, 0, 0, 12, 32, 0, 38, 19, 9, 0, 0, 0, 23, 0, 0, 0, 0, 70, 71, 5, 0, 57, 20, 0, 17, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 28 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

From Robert Israel, Nov 14 2016: (Start)

a(n) < 2*n for n > 1.

If a(n) = 0, then a((2*k+1)*n + k) = 0 for all k >= 0.

(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 = 0..10000

MAPLE

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

  r:= 1; t:= 0;

  for m from 1 do

    r:= r*m mod (2*n+1);

    if r = 0 then return 0 fi;

    t:= t + r mod (2*n+1);

    if t = 0 then return m fi;

  od;

end proc:

f(0):= 1:

map(f, [$0..100]); # Robert Israel, Nov 14 2016

CROSSREFS

Cf. A003422, A013584.

Sequence in context: A124182 A188429 A188430 * A261319 A230414 A053653

Adjacent sequences:  A013582 A013583 A013584 * A013586 A013587 A013588

KEYWORD

nonn

AUTHOR

Michael R. Mudge (Amsorg(AT)aol.com), additional terms from Allan C. Wechsler

STATUS

approved

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Last modified October 19 22:00 EDT 2018. Contains 316378 sequences. (Running on oeis4.)