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A194181
Decimal expansion of the (finite) value of Sum_{k >= 1, k has no even digit in base 10 } 1/k.
3
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
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
KEYWORD
cons,nonn
AUTHOR
Robert G. Wilson v, Aug 18 2011
STATUS
approved