A082830 Decimal expansion of Kempner series Sum_{k>=1, k has no digit 1 in base 10} 1/k.

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

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), 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

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