OFFSET
2,2
COMMENTS
Such sums are called Kempner series, see A082839 (the analog for digit 0) for more information. - M. F. Hasler, Jan 13 2020
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]
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
EXAMPLE
16.17696952812344426657...
MATHEMATICA
(* see the Mmca in Wolfram Library Archive. - Robert G. Wilson v, Jun 01 2009 *)
CROSSREFS
KEYWORD
AUTHOR
Robert G. Wilson v, Apr 14 2003
EXTENSIONS
More terms from Robert G. Wilson v, Jun 01 2009
STATUS
approved