OFFSET
2,1
COMMENTS
Numbers with a digit 8 (A011538) have asymptotic density 1, i.e., here almost all terms are removed from the harmonic series, which makes convergence less surprising. See A082839 (the analog for digit 0) for more information about such so-called Kempner series. - 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.
Eric Weisstein's World of Mathematics, Kempner Series.
Wikipedia, Kempner series.
Wolfram Library Archive, KempnerSums.nb (8.6 KB) - Mathematica Notebook, Summing Kempner's Curious (Slowly-Convergent) Series.
FORMULA
Equals Sum_{k in A052421\{0}} 1/k, where A052421 = numbers with no digit 8. - M. F. Hasler, Jan 14 2020
EXAMPLE
22.726365402679370602833644156742557889210702616360219843536376162... - Robert G. Wilson v, Jun 01 2009
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 and links from Robert G. Wilson v, Jun 01 2009
Minor edits by M. F. Hasler, Jan 13 2020
STATUS
approved