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A073732 Decimal expansion of w = lim n -> infinity n*phi -sum(k=1, n, F(k+1)/F(k) ) where phi is the golden ratio and F(k) denotes the k-th Fibonacci number. 0
3, 1, 8, 4, 5, 2, 9, 6, 4, 0, 7, 4, 5, 0, 1, 0, 8, 1, 2, 9, 2, 1, 7, 5, 7, 2, 1, 3, 2, 6, 2, 4, 7, 6, 3, 9, 9, 3, 6, 1, 8, 7, 8, 2, 2, 7, 3, 0, 7, 5, 8, 3, 5, 2, 0, 9, 9, 0, 6, 4, 2, 6, 5, 9, 8, 4, 3, 4, 6, 8, 7, 8, 2, 6, 2, 1, 9, 0, 3, 3, 1, 1, 9, 0, 4, 9, 6, 5, 4, 1, 9, 6, 4, 5, 8, 2, 9, 6, 8, 7, 7, 0, 4, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

w is also the half of the limit n -> infinity n*sqrt(5) -sum(k=1,n,F(2k)/F(k)^2 )

LINKS

Table of n, a(n) for n=0..103.

FORMULA

w = 0.31845296407450108129217572132624763993618782273...

MATHEMATICA

Clear[f]; f[n_] := f[n] = n *GoldenRatio - Sum[Fibonacci[k + 1]/Fibonacci[k], {k, 1, n}] // RealDigits[#, 10, 104]& // First; f[n=100]; While[f[n] != f[n-100], n = n+100]; f[n] (* Jean-Fran├žois Alcover, Feb 13 2013 *)

CROSSREFS

Sequence in context: A101026 A055249 A125172 * A021318 A068437 A016477

Adjacent sequences:  A073729 A073730 A073731 * A073733 A073734 A073735

KEYWORD

cons,easy,nonn

AUTHOR

Benoit Cloitre, Sep 01 2002

STATUS

approved

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Last modified September 22 00:42 EDT 2020. Contains 337276 sequences. (Running on oeis4.)