

A179954


Decimal expansion of the sum of the reciprocals of pandigital numbers in which each digit appears exactly once.


0



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

0,4


COMMENTS

This is example in 3. 1(a) of R. Baillie, revised.
=0.000825890347919252938607957750178913543253792996588738572977152834596817790608831097159\ 41201897013960993905030473555558175371324365... [From Robert G. Wilson v, Sep 07 2010]
This is a finite sum so it is actually a rational number, although its numerator and denominator are large.


LINKS

Table of n, a(n) for n=0..104.
Robert Baillie, Sums of reciprocals of integers missing a given digit, Amer. Math. Monthly, 86 (1979), 372374.
R. Baillie, Revised Aug 17 2008, Summing The Curious Series Of Kempner and Irwin, arXiv:0806.4410
Wolfram Library Archive, KempnerSums.nb (8.6 KB)  Mathematica Notebook, Summing Kempner's Curious (SlowlyConvergent) Series
Eric Weisstein's World of Mathematics, Digit
Wikipedia, Kempner series


FORMULA

Sum_{ k=1..3265920, 1/A050278(k) }.


EXAMPLE

0.00082589034791925293860795775017891354325379299658873857297715283459681779060883109715...


MATHEMATICA

(* first install irwinSums.m, see either reference, then *) First@ RealDigits@ iSum[{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 64]


CROSSREFS

Cf. A050278, A010784, A082830A082839, A140502, A160502.
Sequence in context: A179048 A173158 A020787 * A197518 A248300 A002994
Adjacent sequences: A179951 A179952 A179953 * A179955 A179956 A179957


KEYWORD

cons,nonn,base


AUTHOR

Robert G. Wilson v, Aug 03 2010


EXTENSIONS

Standardized offset and leading zeros; introduced permanent arXiv URL  R. J. Mathar, Aug 06 2010
More terms from Robert G. Wilson v, Sep 07 2010


STATUS

approved



