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 A082836 Decimal expansion of Kempner series Sum_{k >= 1, k has no digit 7 in base 10} 1/k. 10
 2, 2, 4, 9, 3, 4, 7, 5, 3, 1, 1, 7, 0, 5, 9, 4, 5, 3, 9, 8, 1, 7, 6, 2, 2, 6, 9, 1, 5, 3, 3, 9, 7, 7, 5, 9, 7, 4, 0, 0, 5, 9, 1, 5, 5, 4, 1, 6, 7, 2, 5, 1, 2, 3, 6, 1, 7, 9, 1, 4, 6, 0, 4, 4, 4, 0, 7, 1, 0, 5, 1, 2, 0, 0, 9, 5, 0, 7, 4, 0, 8, 5, 1, 4, 3, 2, 2, 2, 0, 8, 2, 3, 4, 5, 0, 0, 2, 1, 9, 1, 9, 2, 2, 5, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Numbers with a digit 7 (A011537) 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. [Robert G. Wilson v, Jun 01 2009] Eric Weisstein's World of Mathematics, Kempner Series. Wikipedia, Kempner series. [From M. F. Hasler, Jan 13 2020] Wolfram Library Archive, KempnerSums.nb (8.6 KB) - Mathematica Notebook, Summing Kempner's Curious (Slowly-Convergent) Series. [Robert G. Wilson v, Jun 01 2009] FORMULA Equals Sum_{k in A052419\{0}} 1/k, where A052419 = numbers with no digit 7. - M. F. Hasler, Jan 14 2020 EXAMPLE 22.493475311705945398176226915339775974005915541672512361791460444... - Robert G. Wilson v, Jun 01 2009 MATHEMATICA (* see the Mmca in Wolfram Library Archive. - Robert G. Wilson v, Jun 01 2009 *) CROSSREFS Cf. A002387, A024101, A052419 (numbers with no '7'), A011537 (numbers with a '7'). Cf. A082830, A082831, A082832, A082833, A082834, A082835, A082837, A082838, A082839 (analog for digits 1, 2, ..., 9 and 0). Sequence in context: A109214 A000301 A124439 * A201376 A005141 A220369 Adjacent sequences:  A082833 A082834 A082835 * A082837 A082838 A082839 KEYWORD nonn,cons,base AUTHOR Robert G. Wilson v, Apr 14 2003 EXTENSIONS More terms from Robert G. Wilson v, Jun 01 2009 Minor edits by M. F. Hasler, Jan 13 2020 STATUS approved

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Last modified September 20 11:01 EDT 2020. Contains 337264 sequences. (Running on oeis4.)