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A101689
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Decimal expansion of the unique real number x whose Engel expansion is the Fibonacci sequence.
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8
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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
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..102.
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FORMULA
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x = Sum_{n >= 1} 1/(Product_{1 <= i <= n} F(i)), where F(i) is the i-th Fibonacci number.
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EXAMPLE
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x = 2.70450289915406748719754896618187978517783483136...
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MAPLE
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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
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MATHEMATICA
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N[Sum[1/Product[Fibonacci[i], {i, n}], {n, 300}], 100]
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PROG
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(PARI) suminf(n=1, 1/prod(i=1, n, fibonacci(i))) \\ Michel Marcus, Nov 28 2020
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CROSSREFS
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Cf. A000045, A137991 (reciprocal).
Sequence in context: A260129 A341318 A332324 * A175292 A277815 A229178
Adjacent sequences: A101686 A101687 A101688 * A101690 A101691 A101692
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KEYWORD
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cons,nonn
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AUTHOR
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Ryan Propper, Dec 11 2004
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STATUS
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approved
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