A369501 Decimal expansion of the integral of the reciprocal of the Cantor function.

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

Offset: 1

Author

Amiram Eldar, Jan 25 2024

Keywords

• nonn
• cons
• more

Examples

			3.36465072810092516083893496289...
		

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.

Crossrefs

Cf. A001008, A002805, A095844, A095845.

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).