A082830 Decimal expansion of Kempner series Sum_{k>=1, k has no digit 1 in base 10} 1/k.
1, 6, 1, 7, 6, 9, 6, 9, 5, 2, 8, 1, 2, 3, 4, 4, 4, 2, 6, 6, 5, 7, 9, 6, 0, 3, 8, 8, 0, 3, 6, 4, 0, 0, 9, 3, 0, 5, 5, 6, 7, 2, 1, 9, 7, 9, 0, 7, 6, 3, 1, 3, 3, 8, 6, 4, 5, 1, 6, 9, 0, 6, 4, 9, 0, 8, 3, 6, 3, 6, 2, 9, 8, 8, 9, 9, 9, 9, 9, 6, 4, 5, 6, 3, 8, 8, 8, 6, 2, 1, 4, 6, 2, 6, 6, 8, 5, 0, 2, 8, 6, 2, 9, 7, 7
Offset: 2
Examples
16.17696952812344426657...
References
- Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 34.
Links
- Robert Baillie, Sums of reciprocals of integers missing a given digit, Amer. Math. Monthly, 86 (1979), 372-374.
- Robert Baillie, Summing the curious series of Kempner and Irwin, arXiv:0806.4410 [math.CA], 2008-2015. [From _Robert G. Wilson v_, Jun 01 2009]
- Eric Weisstein's World of Mathematics,, Kempner Series. [From _R. J. Mathar_, Aug 07 2010]
- Wikipedia, Kempner series.
- Wolfram Library Archive, KempnerSums.nb (8.6 KB) - Mathematica Notebook, Summing Kempner's Curious (Slowly-Convergent) Series. [From _Robert G. Wilson v_, Jun 01 2009]
Crossrefs
Programs
-
Mathematica
(* see the Mmca in Wolfram Library Archive. - Robert G. Wilson v, Jun 01 2009 *)
Formula
Equals Sum_{k in A052383\{0}} 1/k, where A052383 = numbers with no digit 1. Those which have a digit 1 (A011531) are omitted in the harmonic sum, and they have asymptotic density 1: almost all terms are omitted from the sum. - M. F. Hasler, Jan 15 2020
Extensions
More terms from Robert G. Wilson v, Jun 01 2009
Comments