A052421 -id:A052421 - cp's OEIS frontend

A082837 Decimal expansion of Kempner series Sum_{k >= 1, k has no digit 8 in base 10} 1/k.

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

Offset: 2

Robert G. Wilson v, Apr 14 2003

Numbers with a digit 8 (A011538) 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

			22.726365402679370602833644156742557889210702616360219843536376162... - _Robert G. Wilson v_, Jun 01 2009

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

Robert Baillie, Sums of reciprocals of integers missing a given digit, Amer. Math. Monthly, 86 (1979), 372-374.
Robert Baillie, Summing the curious series of Kempner and Irwin, arXiv:0806.4410 [math.CA], 2008-2015.
Eric Weisstein's World of Mathematics, Kempner Series.
Wikipedia, Kempner series.
Wolfram Library Archive, KempnerSums.nb (8.6 KB) - Mathematica Notebook, Summing Kempner's Curious (Slowly-Convergent) Series.

Cf. A002387, A024101, A052421 (numbers with no '8'), A011538 (numbers with a '8').

Cf. A082830, A082831, A082832, A082833, A082834, A082835, A082836, A082838, A082839 (analog for digits 1, 2, 3, ..., 9 and 0).

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

Equals Sum_{k in A052421\{0}} 1/k, where A052421 = numbers with no digit 8. - M. F. Hasler, Jan 14 2020

More terms and links from Robert G. Wilson v, Jun 01 2009

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

A338287 Decimal expansion of the sum of reciprocals of the numbers that are not pandigital numbers (version 2, A171102).

Original entry on oeis.org

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

Offset: 2

Amiram Eldar, Oct 20 2020

The sum of the reciprocals of the terms of the complement of A171102: numbers with at most 9 distinct digits. It is the union of the 10 sequences of numbers without a single given digit (see the Crossrefs section).

The terms in the data section were taken from the 200 decimal digits given by Strich and Müller (2020).

			65.74331110185328196734583167680868411685344106635398...

Robert Strich and Eric Müller, Ziffernreduzierte Zahlen, in: E. Specht, E. Quaisser and P. Bauermann (eds.), 50 Jahre Bundeswettbewerb Mathematik, Springer Spektrum, Berlin, Heidelberg, 2020, pp. 171-182.

Cf. A171102, A179954, A082830, A082831, A082832, A082833, A082834, A082835, A082836, A082837, A082838, A082839.

Cf. A052382 (numbers without the digit 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).

Equals 1/1 + 1/2 + 1/3 + ... + 1/1023456788 + 1/1023456790 + ..., i.e., A171102(1) = 1023456789 is the first number whose reciprocal is not in the sum.

cp's OEIS Frontend

A082837 Decimal expansion of Kempner series Sum_{k >= 1, k has no digit 8 in base 10} 1/k.

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