A082832 Decimal expansion of Sum_{k >= 1, k has no digit 3 in base 10} 1/k.

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

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

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.

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