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%I #23 Dec 12 2014 10:40:14
%S 1,2,2,6,2,8,4,0,2,4,1,8,2,6,9,0,2,7,4,8,1,4,9,3,7,1,0,0,8,6,2,2,4,0,
%T 3,9,6,1,9,0,8,1,1,4,8,7,3,5,3,6,2,3,5,9,5,5,0,1,6,6,6,5,2,2,1,2,5,2,
%U 7,5,4,3
%N Decimal expansion of the continued fraction c(1) +c(1)/(c(2) +c(2)/(c(3) +c(3)/(c(4) +c(4)/....))), where c(i)=i^2.
%C For more details on this type of continued fractions, see A233588.
%C This one corresponds to the squares of natural numbers.
%H Stanislav Sykora, <a href="/A233591/b233591.txt">Table of n, a(n) for n = 1..20000</a>
%H S. Sykora, <a href="http://dx.doi.org/10.3247/sl4math13.001">Blazys' Expansions and Continued Fractions</a>, Stans Library, Vol.IV, 2013, DOI 10.3247/sl4math13.001
%H S. Sykora, <a href="http://oeis.org/wiki/File:BlazysExpansions.txt">PARI/GP scripts for Blazys expansions and fractions</a>, OEIS Wiki
%F Equals 1+1/(4+4/(9+9/(16+16/(25+25/(36+...))))).
%e 1.22628402418269027481493710086224039619081148735362359550166652...
%t RealDigits[ Fold[(#2 + #2/#1) &, 1, Reverse@ Range[45]^2], 10, 111][[1]] (* _Robert G. Wilson v_, May 22 2014 *)
%o (PARI) See the link
%Y Cf. A000290 (n^2).
%Y Cf. Blazys' continued fractions: A233588, A233589, A233591 and Blazys' expansions: A233582, A233583, A233584, A233585, A233586, A233587.
%K cons,nonn
%O 1,2
%A _Stanislav Sykora_, Jan 06 2014
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