A089729 Decimal expansion of Levy's constant 12*log(2)/Pi^2.

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

Author

Benoit Cloitre, Jan 19 2004

Keywords

• nonn
• cons

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

Examples

			0.8427659132721945169072631939639641155945183893191504965...
		

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

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Harmonic Number
• Eric Weisstein's World of Mathematics, Levy Constant

Crossrefs

Cf. A086702, A086237.

Programs

Mathematica

RealDigits[12 Log[2]/Pi^2, 10, 100][[1]] (* Bruno Berselli, Jun 20 2013 *)

PARI

12*log(2)/Pi^2 \\ Michel Marcus, Mar 23 2016

Extensions

Leading zero removed by R. J. Mathar, Feb 05 2009