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
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