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A338304
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Decimal expansion of Sum_{k>=0} 1/L(2^k), where L(k) is the k-th Lucas number (A000032).
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3
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1, 4, 9, 7, 9, 2, 0, 3, 8, 0, 9, 9, 9, 0, 6, 2, 7, 1, 9, 8, 7, 0, 6, 8, 5, 5, 5, 3, 9, 9, 2, 8, 5, 9, 6, 0, 8, 0, 7, 2, 0, 7, 7, 1, 9, 8, 5, 7, 0, 8, 5, 9, 7, 0, 4, 0, 4, 9, 3, 2, 2, 3, 9, 8, 9, 5, 4, 0, 5, 2, 7, 7, 6, 9, 5, 3, 2, 2, 3, 7, 8, 3, 9, 9, 3, 2, 1
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OFFSET
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1,2
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COMMENTS
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Erdős and Graham (1980) asked whether this constant is irrational or transcendental.
Badea (1987) proved that it is irrational, and André-Jeannin (1991) proved that it is not a quadratic irrational in Q(sqrt(5)), in contrast to the corresponding sum with Fibonacci numbers, Sum_{k>=0} 1/F(2^k) = (7-sqrt(5))/2 (A079585).
Bundschuh and Pethö (1987) proved that it is transcendental.
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LINKS
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FORMULA
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Equals 1 + Sum_{k>=0} 1/A001566(k).
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EXAMPLE
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1.49792038099906271987068555399285960807207719857085...
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MATHEMATICA
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RealDigits[Sum[1/LucasL[2^n], {n, 0, 10}], 10, 100][[1]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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