A261390 - OEIS

A261390

2 * Sum_{n>=3} 1/Fibonacci(n).

2, 7, 1, 9, 7, 7, 1, 3, 3, 2, 4, 8, 6, 3, 5, 5, 1, 0, 6, 3, 4, 4, 0, 2, 2, 6, 0, 5, 8, 3, 7, 8, 5, 4, 3, 5, 9, 3, 7, 7, 8, 1, 0, 2, 6, 7, 4, 6, 3, 9, 3, 6, 9, 7, 2, 9, 9, 1, 1, 0, 7, 6, 3, 0, 6, 5, 0, 2, 6, 0, 6, 3, 7, 9, 9, 3, 3, 6, 6, 7, 6, 7, 2, 3, 0, 8, 3, 2, 4, 3, 2, 9, 1, 3, 5, 8, 0, 1, 7, 4, 5, 9, 4, 0, 9

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OFFSET

1,1

COMMENTS

Also the decimal expansion of the sum of the reciprocals of averages of adjacent pairs of Fibonacci numbers: Sum_{n>=1} 2/(A000045(n) + A000045(n+1)).

LINKS

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

Matematico Fresnillense, Constante suma inversos de promedios de Números Fibonacci

FORMULA

Equals 2*A079586 - 4. - Michel Marcus, Aug 18 2015

EXAMPLE

2.719771332486355106344022605837854359377810267463936972991107630650260637993...

MATHEMATICA

adjFibAvRecipSum = Table[Sum[2/(Fibonacci[n] + Fibonacci[n + 1]), {n, 1000}]]; N[adjFibAvRecipSum, 20]

s = 0; k = 1; a = 2; b = 3; While[k < 525, s = N[s + 1/a, 128]; k++; {a, b} = {b, a + b}]; RealDigits[ 2s, 10, 111][[1]] (* Robert G. Wilson v, Aug 21 2015 *)

PROG

(PARI) suminf(n=3, 2/fibonacci(n)) \\ Charles R Greathouse IV, Aug 20 2015

CROSSREFS

Cf. A000045, A079586.

Sequence in context: A112257 A248684 A175728 * A248676 A369445 A330914

Adjacent sequences: A261387 A261388 A261389 * A261391 A261392 A261393

KEYWORD

nonn,cons

AUTHOR

José de Jesús Camacho Medina, Aug 17 2015

STATUS

approved