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A101689 Decimal expansion of the unique real number x whose Engel expansion is the Fibonacci sequence. 8
2, 7, 0, 4, 5, 0, 2, 8, 9, 9, 1, 5, 4, 0, 6, 7, 4, 8, 7, 1, 9, 7, 5, 4, 8, 9, 6, 6, 1, 8, 1, 8, 7, 9, 7, 8, 5, 1, 7, 7, 8, 3, 4, 8, 3, 1, 3, 6, 0, 6, 2, 8, 1, 6, 9, 2, 1, 6, 1, 4, 7, 1, 7, 9, 7, 0, 5, 7, 9, 7, 4, 3, 2, 7, 7, 3, 3, 8, 2, 7, 7, 3, 0, 0, 3, 7, 3, 4, 8, 9, 3, 2, 4, 6, 4, 7, 5, 8, 1, 1, 9, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

x = Sum_{n >= 1} 1/(Product_{1 <= i <= n} F(i)), where F(i) is the i-th Fibonacci number.

EXAMPLE

x = 2.70450289915406748719754896618187978517783483136...

MAPLE

with(combinat); P:=proc(q)

evalf(add(mul(1/fibonacci(i), i=1..k), k=1..q), 200); end: # Paolo P. Lava, Feb 13 2014

MATHEMATICA

N[Sum[1/Product[Fibonacci[i], {i, n}], {n, 300}], 100]

PROG

(PARI) suminf(n=1, 1/prod(i=1, n, fibonacci(i))) \\ Michel Marcus, Nov 28 2020

CROSSREFS

Cf. A000045, A137991 (reciprocal).

Sequence in context: A260129 A341318 A332324 * A175292 A277815 A229178

Adjacent sequences:  A101686 A101687 A101688 * A101690 A101691 A101692

KEYWORD

cons,nonn

AUTHOR

Ryan Propper, Dec 11 2004

STATUS

approved

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Last modified April 15 20:40 EDT 2021. Contains 342977 sequences. (Running on oeis4.)