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A065444
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Decimal expansion of 9*Sum{k=1..inf} 1/(10^k-1).
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5
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1, 1, 0, 0, 9, 1, 8, 1, 9, 0, 8, 3, 6, 2, 0, 0, 7, 3, 6, 3, 7, 9, 8, 5, 5, 1, 0, 1, 6, 5, 4, 3, 8, 0, 0, 4, 3, 2, 0, 3, 4, 5, 4, 3, 9, 7, 8, 7, 3, 2, 8, 1, 6, 5, 6, 3, 5, 9, 8, 9, 0, 2, 2, 0, 7, 3, 4, 3, 8, 3, 4, 9, 0, 2, 1, 9, 8, 3, 4, 7, 4, 8, 8, 9, 2, 0, 0, 3, 4, 9, 2, 1, 8, 0, 0, 7, 0, 4, 0, 2, 3, 5
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| a(n) is the infinite sum of the reciprocals of repunits, R_n, with n>0 (A002275) [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Dec 06 2009]
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REFERENCES
| S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,2000
S. R. Finch, Digital Search Tree Constants
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EXAMPLE
| 1.10091819083620073637985510165438004320345439787328165635989...
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MATHEMATICA
| RealDigits[9*N[ Sum[1/(10^k - 1), {k, 1, Infinity}], 120]] [[1]]
A065444=RealDigits[ Block[{$MaxExtraPrecision = 100}, N[9*Sum[(-1 + 10^i)^-1, {i, 1, Infinity}], 130]]][[1]] [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Dec 06 2009]
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PROG
| (PARI) { default(realprecision, 2080); x=9*suminf(k=1, 1/(10^k - 1)); for (n=1, 2000, d=floor(x); x=(x-d)*10; write("b065444.txt", n, " ", d)) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 19 2009]
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CROSSREFS
| Equals 9*A073668.
A067617 gives the expansion in continued fraction of a(n) [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Dec 06 2009]
Sequence in context: A154207 A200101 A084002 * A010169 A113657 A098783
Adjacent sequences: A065441 A065442 A065443 * A065445 A065446 A065447
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KEYWORD
| nonn,cons
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 18 2001
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EXTENSIONS
| More terms from John W. Layman (layman(AT)math.vt.edu), Nov 19 2001
...733 (50th digit) expanded to ...7328165 etc. by Frank Ellermann (hmdmhdfmhdjmzdtjmzdtzktdkztdjz(AT)gmail.com), Feb 23 2002
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