A112365 Least multiple of n such that every partial sum is a Fibonacci number.

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.

Links

Table of n, a(n) for n=1..15.

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

Crossrefs

Cf. A112366.

Sequence in context: A078837 A232155 A368755 * A242200 A258929 A034959

Adjacent sequences: A112362 A112363 A112364 * A112366 A112367 A112368

Keyword

nonn

Author

Amarnath Murthy, Sep 09 2005

Extensions

More terms from R. J. Mathar, Aug 24 2007

Status

approved