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%I #15 May 20 2024 14:04:09
%S 1,2,18,68,55,46224,2131941,163401832,139418282304,17028096315120,
%T 2094317397800485,12198048930043898688,1488320375791774206539,
%U 4855786456799950164906,178195518800026250118150
%N Least multiple of n such that every partial sum is a Fibonacci number.
%C The idea derived from the fact that the sequence of natural numbers gives the least multiple of n such that every partial sum is a triangular number.
%e 1, 1+2 = 3, 1+2+18 = 21 are all Fibonacci numbers.
%p A112365 := proc(nmin) local a,psum,n,k,i ; a := [] ; psum := 0 ; for n from 1 to nmin do i := 1 ; while combinat[fibonacci](i)-psum <= 0 or (combinat[fibonacci](i)-psum) mod n <> 0 do i := i+1 ; od ; k := (combinat[fibonacci](i)-psum)/n ; a := [op(a),k*n] ; psum := psum+k*n ; od; RETURN(a) ; end: op(A112365(40)) ; # _R. J. Mathar_, Aug 24 2007
%t A112365[nmin_] := Module[{a, psum, n, k, i}, a = {}; psum = 0; For[n = 1, n <= nmin, n++, i = 1; While[Fibonacci[i] - psum <= 0 || (Fibonacci[i] - psum) ~Mod~ n != 0, i++]; k = (Fibonacci[i] - psum)/n; a = Append[a, k*n]; psum += k*n]; Return[a]];
%t A112365[40] (* _Jean-François Alcover_, May 20 2024, after _R. J. Mathar_ *)
%Y Cf. A112366.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Sep 09 2005
%E More terms from _R. J. Mathar_, Aug 24 2007
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