login
A089729
Decimal expansion of Levy's constant 12*log(2)/Pi^2.
7
8, 4, 2, 7, 6, 5, 9, 1, 3, 2, 7, 2, 1, 9, 4, 5, 1, 6, 9, 0, 7, 2, 6, 3, 1, 9, 3, 9, 6, 3, 9, 6, 4, 1, 1, 5, 5, 9, 4, 5, 1, 8, 3, 8, 9, 3, 1, 9, 1, 5, 0, 4, 9, 6, 5, 2, 9, 2, 1, 2, 5, 3, 8, 7, 3, 8, 9, 9, 5, 6, 9, 6, 0, 4, 3, 6, 2, 2, 4, 0, 8, 1, 7, 0, 4, 2, 0, 3, 2, 2, 9, 6, 8, 8, 0, 0, 8, 1, 1, 3, 1, 9, 3, 1, 4
OFFSET
0,1
COMMENTS
For x>y in [1..n], the average number of loop steps of the Euclid Algorithm for GCD (over all choices x, y) is asymptotic to k*log(n) where k is this constant. See Crandall & Pomerance. - Michel Marcus, Mar 23 2016
REFERENCES
R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see Theorem 2.1.3, p. 84.
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 156.
LINKS
Eric Weisstein's World of Mathematics, Harmonic Number
Eric Weisstein's World of Mathematics, Levy Constant
EXAMPLE
0.8427659132721945169072631939639641155945183893191504965...
MATHEMATICA
RealDigits[12 Log[2]/Pi^2, 10, 100][[1]] (* Bruno Berselli, Jun 20 2013 *)
PROG
(PARI) 12*log(2)/Pi^2 \\ Michel Marcus, Mar 23 2016
CROSSREFS
Sequence in context: A348908 A014391 A099286 * A173670 A337170 A050135
KEYWORD
nonn,cons
AUTHOR
Benoit Cloitre, Jan 19 2004
EXTENSIONS
Leading zero removed by R. J. Mathar, Feb 05 2009
STATUS
approved