A194181 Decimal expansion of the (finite) value of Sum_{k >= 1, k has no even digit in base 10 } 1/k.

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

Offset

1,1

Comments

For an elementary proof that this series is convergent, see Honsberger's reference. - Bernard Schott, Jan 13 2022

References

Ross Honsberger, Mathematical Gems II, Dolciani Mathematical Expositions No. 2, Mathematical Association of America, 1976, pp. 102 and 177.

Links

Table of n, a(n) for n=1..101.

Robert Baillie and Thomas Schmelzer, Summing Kempner's Curious (Slowly-Convergent) Series, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.

Thomas Schmelzer and Robert Baillie, Summing a curious, slowly convergent, harmonic subseries, American Mathematical Monthly 115:6 (2008), pp. 525-540; preprint.

Wikipedia, Kempner series.

Formula

Equals Sum_{n>=1} 1/A014261(n). - Bernard Schott, Jan 13 2022

Example

3.17176547341590495722870970875061165679705070839628572416418689843...

Mathematica

RealDigits[kSum[{0, 2, 4, 6, 8}, 120 ]][[1]] (* Amiram Eldar, Jun 15 2023, using Baillie and Schmelzer's kempnerSums.nb, see Links *)

Crossrefs

Cf. A014261, A082830, A194182.

Sequence in context: A323599 A167515 A140435 * A277934 A063754 A163117

Adjacent sequences: A194178 A194179 A194180 * A194182 A194183 A194184

Keyword

cons,nonn

Author

Robert G. Wilson v, Aug 18 2011

Status

approved