OFFSET
1,3
COMMENTS
"(By strange coincidence, the information in a typical continued fraction term is very nearly one decimal digit - actually pi^2/(6 (ln 2) (ln 10)) = 1.0306.) R. W. Gosper. Math-Fun list, April 9, 1998. This constant is the average number of decimal digits necessary to have the equivalent continued fraction representations of a number in base 10. In other words if you have N decimal digits it will give you N/C = N/1.0306 valid partial quotients in average." - Simon Plouffe
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.8 Khintchine-Lévy constants, p. 60.
LINKS
Simon Plouffe, Plouffe's Inverter
Eric Weisstein's World of Mathematics, Lochs' Theorem
FORMULA
Pi^2/(6 (log 2) (log 10)).
EXAMPLE
1.03064083410071293588177609411693684092592031112072628177006095223495442800479...
MATHEMATICA
RealDigits[Pi^2/(6Log[2]Log[10]), 10, 120][[1]] (* Harvey P. Dale, Apr 11 2012 *)
CROSSREFS
KEYWORD
AUTHOR
Jason Earls, Jun 25 2001
STATUS
approved