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%I #18 Dec 15 2017 17:35:12
%S 1,0,3,0,6,4,0,8,3,4,1,0,0,7,1,2,9,3,5,8,8,1,7,7,6,0,9,4,1,1,6,9,3,6,
%T 8,4,0,9,2,5,9,2,0,3,1,1,1,2,0,7,2,6,2,8,1,7,7,0,0,6,0,9,5,2,2,3,4,9,
%U 5,4,4,2,8,0,0,4,7,9,9,7,6,7,5,1,8,3,6,0,8,0,8,3,9,5,6,5,8,6,5,4,7,6,2,6,3
%N Decimal expansion of the continued fraction constant (base 10).
%C "(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_
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.8 Khintchine-Lévy constants, p. 60.
%H Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/continuedfr.txt">Plouffe's Inverter</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LochsTheorem.html">Lochs' Theorem</a>
%F Pi^2/(6 (log 2) (log 10)).
%e 1.03064083410071293588177609411693684092592031112072628177006095223495442800479...
%t RealDigits[Pi^2/(6Log[2]Log[10]),10,120][[1]] (* _Harvey P. Dale_, Apr 11 2012 *)
%Y Cf. A062543.
%K cons,easy,nonn
%O 1,3
%A _Jason Earls_, Jun 25 2001
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