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A369501
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Decimal expansion of the integral of the reciprocal of the Cantor function.
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0
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3, 3, 6, 4, 6, 5, 0, 7, 2, 8, 1, 0, 0, 9, 2, 5, 1, 6, 0, 8, 3, 8, 9, 3, 4, 9, 6, 2, 8, 9
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OFFSET
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1,1
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LINKS
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Harold G. Diamond and Bruce Reznick, Problem 10621, Problems and Solutions, The American Mathematical Monthly, Vol. 104, No. 9 (1997), p. 870; Cantor's Singular Moments, Solutions to Problem 10621 by Kenneth F. Andersen and Omran Kouba, ibid., Vol. 106, No. 2 (1999), pp. 175-176.
Helmut Prodinger, Digits and beyond, in: B. Chauvin, P. Flajolet, D. Gardy, and A. Mokkadem (eds.), Mathematics and Computer Science II: Algorithms, Trees, Combinatorics and Probabilities, Birkhäuser, Basel (2012), pp. 355-377.
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FORMULA
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Equals Integral_{x=0..1} (1/c(x)) dx, where c(x) is the Cantor function.
Equals Sum_{k>=0} Integral_{x=0..1} c(x)^k dx = Sum_{k>=0} A095844(k)/A095845(k) (Javier Duoandikoetx, in "Cantor's Singular Moments", 1999).
Equals -1/3 + (2/3) * Sum_{k>=1} (2/3)^k * H(2^k), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number (Prodinger, 2000).
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EXAMPLE
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3.36465072810092516083893496289...
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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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