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A290565 Decimal expansion of sum of reciprocal golden rectangle numbers. 4
1, 7, 7, 3, 8, 7, 7, 5, 8, 3, 2, 8, 5, 1, 3, 2, 3, 4, 3, 8, 0, 2, 3, 6, 2, 7, 6, 5, 6, 7, 6, 9, 6, 5, 9, 2, 2, 8, 3, 0, 7, 2, 3, 2, 3, 9, 3, 5, 9, 4, 3, 4, 1, 1, 0, 8, 3, 9, 2, 2, 9, 0, 4, 9, 8, 6, 4, 9, 2, 2, 0, 7, 5, 3, 0, 3, 8, 5, 1, 1, 9, 4, 7, 0, 3, 6, 2, 4, 3, 3, 3, 8, 6, 0, 5, 2, 6, 4, 2, 6, 9, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The constant k in A277266 such that A277266(n) ~ k*n.

LINKS

Table of n, a(n) for n=1..102.

FORMULA

Equals Sum_{n>=1} 1/(Fibonacci(n)*Fibonacci(n+1)).

Equals lim n->infinity A277266(n)/n.

EXAMPLE

1/(1*1) + 1/(1*2) + 1/(2*3) + 1/(3*5) + ... = 1 + 1/2 + 1/6 + 1/15 + ... = 1.77387758328513234380...

MATHEMATICA

RealDigits[ Sum[1/(Fibonacci[k]*Fibonacci[k + 1]), {k, 265}], 10, 111][[1]]

PROG

(PARI) suminf(n=1, 1/(fibonacci(n)*fibonacci(n+1))) \\ Michel Marcus, Feb 19 2019

CROSSREFS

Cf. A000045, A001654, A277266.

Cf. A079586.

Sequence in context: A063736 A212299 A193751 * A319263 A318386 A318334

Adjacent sequences:  A290562 A290563 A290564 * A290566 A290567 A290568

KEYWORD

cons,nonn

AUTHOR

Bobby Jacobs and Robert G. Wilson v, Aug 06 2017

EXTENSIONS

More terms from Alois P. Heinz, Aug 06 2017

STATUS

approved

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Last modified December 12 07:31 EST 2019. Contains 329948 sequences. (Running on oeis4.)