The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A082832 Decimal expansion of Sum_{k >= 1, k has no digit 3 in base 10} 1/k. 11
 2, 0, 5, 6, 9, 8, 7, 7, 9, 5, 0, 9, 6, 1, 2, 3, 0, 3, 7, 1, 0, 7, 5, 2, 1, 7, 4, 1, 9, 0, 5, 3, 1, 1, 1, 4, 1, 4, 1, 5, 3, 8, 6, 9, 6, 7, 4, 7, 3, 0, 7, 8, 3, 4, 8, 9, 5, 0, 8, 5, 2, 8, 5, 0, 0, 2, 6, 7, 2, 9, 4, 9, 9, 6, 1, 9, 3, 8, 0, 3, 5, 0, 0, 5, 9, 0, 4, 7, 4, 9, 4, 0, 8, 0, 6, 0, 3, 5, 3, 4, 9, 8, 7, 9, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Numbers with a digit 3 (A011533) have asymptotic density 1, i.e., 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. [From 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. [From Robert G. Wilson v, Jun 01 2009] FORMULA Equals Sum_{k in A052405\{0}} 1/k, where A052405 = numbers with no digit 3. - M. F. Hasler, Jan 15 2020 EXAMPLE 20.569877950961230371075217419053111414153869674730783489508528500... - 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, A052405 (numbers with no '3'), A011533 (numbers with '3'). Cf. A082830, A082831, A082833, A082834, A082835, A082836, A082837, A082838, A082839 (analog for digits 1, 2, 4, ..., 9 and 0). Sequence in context: A262420 A240662 A188724 * A334842 A320372 A097709 Adjacent sequences:  A082829 A082830 A082831 * A082833 A082834 A082835 KEYWORD nonn,cons,base AUTHOR Robert G. Wilson v, Apr 14 2003 EXTENSIONS More terms from Robert G. Wilson v, Jun 01 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 12 16:55 EDT 2021. Contains 344959 sequences. (Running on oeis4.)