A082831 Decimal expansion of Sum_{k >= 1, k has no digit 2 in base 10} 1/k.

1, 9, 2, 5, 7, 3, 5, 6, 5, 3, 2, 8, 0, 8, 0, 7, 2, 2, 2, 4, 5, 3, 2, 7, 7, 6, 7, 7, 0, 1, 9, 4, 4, 5, 4, 1, 1, 5, 5, 2, 6, 0, 5, 3, 8, 3, 1, 1, 5, 4, 8, 7, 0, 1, 4, 9, 8, 6, 8, 3, 6, 2, 9, 4, 9, 1, 0, 4, 3, 0, 9, 0, 1, 6, 0, 1, 9, 5, 5, 1, 8, 0, 9, 2, 8, 0, 5, 4, 6, 2, 2, 1, 1, 2, 8, 4, 4, 2, 8, 6, 3, 5, 5, 6, 5

Offset

2,2

Comments

Such sums are called Kempner series, see A082839 (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.

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 A052404\{0}} 1/k, where A052404 = numbers with no digit 2: these are omitted in the harmonic series. - M. F. Hasler, Jan 13 2020

Example

19.25735653280807222453277677019445411552605383115487014986836294...

Mathematica

(* see the Mmca in Wolfram Library Archive *)

Crossrefs

Cf. A002387, A024101, A052404 (numbers with no digit 2).

Cf. A082830, A082832, A082833, A082834, A082835, A082836, A082837, A082838, A082839 (analog for digits 1, 3, 4, ..., 9 and 0).

Sequence in context: A342574 A154838 A378388 * A085551 A316328 A323809

Adjacent sequences: A082828 A082829 A082830 * A082832 A082833 A082834

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