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

Author

Robert G. Wilson v, Aug 18 2011

Keywords

• cons
• nonn

Comments

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

Examples

			3.17176547341590495722870970875061165679705070839628572416418689843...
		

References

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

Links

• 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.

Crossrefs

Cf. A014261, A082830, A194182.

Programs

Mathematica

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

Formula

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