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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 MATHEMATICA a[n_] := Module[{t, r, m}, r = 1; t = 0; For[m = 1, True, m++, r = Mod[r m, 2 n + 1]; If[r == 0, Return[0]]; t = Mod[t + r, 2 n + 1]; If[t == 0, Return[m]]]]; a[0] = 1; a /@ Range[0, 100] (* Jean-François Alcover, Jul 19 2020, after Maple *) 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 August 9 12:34 EDT 2022. Contains 356026 sequences. (Running on oeis4.)