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A112365
Least multiple of n such that every partial sum is a Fibonacci number.
2
1, 2, 18, 68, 55, 46224, 2131941, 163401832, 139418282304, 17028096315120, 2094317397800485, 12198048930043898688, 1488320375791774206539, 4855786456799950164906, 178195518800026250118150
OFFSET
1,2
COMMENTS
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.
EXAMPLE
1, 1+2 = 3, 1+2+18 = 21 are all Fibonacci numbers.
MAPLE
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
MATHEMATICA
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]];
A112365[40] (* Jean-François Alcover, May 20 2024, after R. J. Mathar *)
CROSSREFS
Cf. A112366.
Sequence in context: A078837 A232155 A368755 * A242200 A258929 A034959
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Sep 09 2005
EXTENSIONS
More terms from R. J. Mathar, Aug 24 2007
STATUS
approved