%I #17 Nov 14 2014 11:27:54
%S 1,5,2,4,9,6,5,3,4,4,4,1,7,8,9,4,9,1,2,8,2,1,2,2,3,0,9,4,0,6,2,5,5,6,
%T 2,3,2,4,6,8,4,6,0,4,2,9,9,9,9,4,6,8,1,1,5,3,6,9,2,1,1,5,0,9,1,2,8,2,
%U 6,8,4,4,7,6,2,0,5,0,1,7,4,7,9,7,5,6,4,9,8,4,9,4,4,3,5,0,1,3,5,4,4,8,6,9,4
%N Decimal expansion of the constant 1+3/(5+7/(9+11/(13+...))), using all odd integers in this generalized continued fraction.
%C The (simple) continued fraction of this constant is [1;1,1,9,1,1,17,1,1,25,...], every 3rd term being of the form 8n+1.
%e 1.524965344417894912821223094...
%p r:= (n, i)-> n+ `if`(i<1, 1, (n+2)/r(n+4, i-1)):
%p s:= convert(evalf(r(1, 80)/10, 130), string):
%p seq(parse(s[n+1]), n=1..120); # _Alois P. Heinz_, Oct 16 2011
%t digits = 105; f[n_] := f[n] = Fold[#2 + (#2+2)/#1 &, 4*n+1, Range[4*n-3, 1, -4] ] // RealDigits[#, 10, digits]& // First; f[digits]; f[n = 2*digits]; While[f[n] != f[n/2], n = 2*n]; f[n] (* _Jean-François Alcover_, Feb 21 2014 *)
%Y Cf. A113011.
%K cons,nonn
%O 1,2
%A _Jonathan D. B. Hodgson_, Oct 01 2010
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