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A236145
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Records in the continued fraction expansion of Sum_{k >= 2} 2^(-Fibonacci(k)) (A006518).
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0
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1, 10, 14, 124, 2039, 262111, 536870655, 140737488347135, 75557863725914321321983, 10633823966279326983230456465062887423, 803469022129495137770981046170581301261101460862599398686719
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OFFSET
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1,2
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COMMENTS
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Positions of records are at 2, 7, 9, 13, 19, 27, 35, 47, 63, 87, 117, 159, 217, 301, 413, ...
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LINKS
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FORMULA
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Conjecture: For n>4, a(n) = 2^L(n) - 2^F(n) - 1, with L(n) the Lucas numbers A000032, and F(n) the Fibonacci numbers.
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MATHEMATICA
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Rest[DeleteDuplicates[ContinuedFraction[Sum[2^-Fibonacci[k], {k, 2, 20}]], GreaterEqual]] (* Harvey P. Dale, Sep 04 2023 *)
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PROG
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(PARI) m=1; for(n=1, 500, t=contfrac(suminf(i=2, 1/2^fibonacci(i)))[n+1]; if(m<t, m=t; print1(t, ", ")))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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