cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A082835 Decimal expansion of Kempner series Sum_{k >= 1, k has no digit 6 in base 10} 1/k.

Original entry on oeis.org

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

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Author

Robert G. Wilson v, Apr 14 2003

Keywords

Comments

Numbers with a digit 6 (A011536) have asymptotic density 1, i.e., here 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

Examples

			22.20559815955609188416738048000752710519385610666846327027693823... - _Robert G. Wilson v_, Jun 01 2009

References

  • Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 34.

Links

Crossrefs

Cf. A002387, A024101, A052414 (numbers with no '6'), A011536 (numbers with a '6').
Cf. A082830, A082831, A082832, A082833, A082834, A082836, A082837, A082838, A082839 (analog for digits 1, 2, 4, ..., 9 and 0).

Programs

  • Mathematica
    (* see the Mmca in Wolfram Library Archive. - Robert G. Wilson v, Jun 01 2009 *)

Formula

Equals Sum_{k in A052414\{0}} 1/k, where A052414 = numbers with no digit 6. - M. F. Hasler, Jan 15 2020

Extensions

Minor edits by M. F. Hasler, Jan 13 2020

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