

A082830


Decimal expansion of Kempner series Sum_{k>=1, k has no digit 1 in base 10} 1/k.


14



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
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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

Table of n, a(n) for n=2..106.
Robert Baillie, Sums of reciprocals of integers missing a given digit, Amer. Math. Monthly, 86 (1979), 372374.
Robert Baillie, Summing the curious series of Kempner and Irwin, arXiv:0806.4410 [math.CA], 20082015. [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 (SlowlyConvergent) 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

Cf. A002387, A024101, A052383 (numbers without '1'), A011531 (numbers with '1').
Cf. A082831, A082832, A082833, A082834, A082835, A082836, A082837, A082838, A082839 (analog for digits 2, ..., 9 and 0).
Sequence in context: A110942 A274014 A334962 * A261622 A046902 A204205
Adjacent sequences: A082827 A082828 A082829 * A082831 A082832 A082833


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



