|
| |
|
|
A194181
|
|
Decimal expansion of the (finite) value of the 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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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.
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...
|
|
|
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
|
| |
|
|
