OFFSET
1,2
COMMENTS
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.
EXAMPLE
1.524965344417894912821223094...
MAPLE
r:= (n, i)-> n+ `if`(i<1, 1, (n+2)/r(n+4, i-1)):
s:= convert(evalf(r(1, 80)/10, 130), string):
seq(parse(s[n+1]), n=1..120); # Alois P. Heinz, Oct 16 2011
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Jonathan D. B. Hodgson, Oct 01 2010
STATUS
approved