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A369501 Decimal expansion of the integral of the reciprocal of the Cantor function. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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.
Steven Finch, Cantor-solus and Cantor-multus Distributions, arXiv:2003.09458 [math.CO], 2020.
Russell A. Gordon, Some Integrals Involving the Cantor Function, The American Mathematical Monthly, Vol. 116, No. 3 (2009), pp. 218-227; alternative link.
Helmut Prodinger, On Cantor's singular moments, Southwest Journal of Pure and Applied Mathematics, Vol. 2000, Issue 1 (July 2000), pp. 27-29; arXiv preprint, arXiv:math/9904072 [math.CO], 1999.
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.
Eric Weisstein's World of Mathematics, Cantor Function.
Wikipedia, Cantor function.
FORMULA
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).
EXAMPLE
3.36465072810092516083893496289...
CROSSREFS
Sequence in context: A143305 A051472 A257957 * A324000 A048149 A155169
KEYWORD
nonn,cons,more
AUTHOR
Amiram Eldar, Jan 25 2024
STATUS
approved

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Last modified September 9 10:11 EDT 2024. Contains 375764 sequences. (Running on oeis4.)