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 A065444 Decimal expansion of 9*Sum_{k>=1} 1/(10^k-1). 5
 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; text; internal format)
 OFFSET 1,5 COMMENTS This constant is the infinite sum of the reciprocals of repunits, R_n, with n>0 (A002275). - Enrique Pérez Herrero, Dec 06 2009 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361. LINKS Harry J. Smith, Table of n, a(n) for n=1..2000 Steven R. Finch, Digital Search Tree Constants [Broken link] Steven R. Finch, Digital Search Tree Constants [From the Wayback machine] FORMULA Equals 9 * sum(k>=1, (1+x^k)/(1-x^k) * x^(k^2) ) where x = 1/10.  This allows fast computation for this and similar sequences (involving sum(k>=1, x^k/(1-x^k) for some x < 1 ). - Joerg Arndt, Apr 25 2016 EXAMPLE 1.10091819083620073637985510165438004320345439787328165635989... 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]] (* Enrique Pérez Herrero, Dec 06 2009 *) First[RealDigits[9 (Log10[10/9] - QPolyGamma[0, 1, 1/10]/Log[10]), 10, 120]] (* Jan Mangaldan, Apr 25 2016 *) 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)) } \\ Harry J. Smith, Oct 19 2009 CROSSREFS Equals 9*A073668. Cf. A067617 (continued fraction). Sequence in context: A084002 A339605 A182494 * A010169 A113657 A098783 Adjacent sequences:  A065441 A065442 A065443 * A065445 A065446 A065447 KEYWORD nonn,cons AUTHOR N. J. A. Sloane, Nov 18 2001 EXTENSIONS More terms from John W. Layman, Nov 19 2001 ...733 (50th digit) expanded to ...7328165 etc. by Frank Ellermann, Feb 23 2002 STATUS approved

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Last modified April 18 02:38 EDT 2021. Contains 343072 sequences. (Running on oeis4.)