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A153386 Decimal expansion of Sum_{n>=1} 1/Fibonacci(2*n). 5
1, 5, 3, 5, 3, 7, 0, 5, 0, 8, 8, 3, 6, 2, 5, 2, 9, 8, 5, 0, 2, 9, 8, 5, 2, 8, 9, 6, 6, 5, 1, 5, 9, 9, 0, 0, 6, 3, 6, 7, 0, 1, 1, 5, 9, 1, 0, 7, 1, 1, 3, 8, 5, 6, 3, 2, 3, 5, 2, 6, 3, 6, 6, 5, 1, 3, 1, 0, 4, 7, 2, 7, 8, 6, 2, 8, 9, 0, 9, 4, 1, 6, 0, 1, 6, 5, 0, 2, 3, 1, 6, 6, 3, 6, 9, 6, 9, 3, 3, 6, 5, 3, 2, 7, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..105.

A. F. Horadam, Elliptic Functions and Lambert Series in the Summation of Reciprocals in Certain Recurrence-Generated Sequences, The Fibonacci Quarterly, Vol. 26, No. 2 (1988), pp. 98-114.

FORMULA

Equals sqrt(5) * (L((3-sqrt(5))/2) - L((7-3*sqrt(5))/2)), where L(x) = Sum_{k>=1} x^k/(1-x^k) (Horadam, 1988). - Amiram Eldar, Oct 04 2020

EXAMPLE

1.5353705088362529850...

MATHEMATICA

rd[k_] := rd[k] = RealDigits[ N[ Sum[ 1/Fibonacci[2*n], {n, 1, 2^k}], 105]][[1]]; rd[k = 4]; While[ rd[k] != rd[k - 1], k++]; rd[k] (* Jean-François Alcover, Oct 29 2012 *)

CROSSREFS

Cf. A079586, A153387.

Sequence in context: A270915 A319461 A201762 * A112920 A109364 A122277

Adjacent sequences:  A153383 A153384 A153385 * A153387 A153388 A153389

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Dec 25 2008

STATUS

approved

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Last modified January 16 17:26 EST 2021. Contains 340206 sequences. (Running on oeis4.)