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Search: id:A112365
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| A112365 |
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Least multiple of n so that every partial sum is a Fibonacci number. |
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+0
2
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| 1, 2, 18, 68, 55, 46224, 2131941, 163401832, 139418282304, 17028096315120, 2094317397800485, 12198048930043898688, 1488320375791774206539, 4855786456799950164906, 178195518800026250118150
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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EXAMPLE
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1,1+2 =3, 1+2+18 =21 are all Fibonacci numbers.
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MAPLE
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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 (mathar(AT)strw.leidenuniv.nl), Aug 24 2007
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CROSSREFS
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Cf. A112366.
Adjacent sequences: A112362 A112363 A112364 this_sequence A112366 A112367 A112368
Sequence in context: A085293 A119118 A078837 this_sequence A034959 A073976 A120361
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 09 2005
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 24 2007
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