A181050 Decimal expansion of the constant 1+3/(5+7/(9+11/(13+...))), using all odd integers in this generalized continued fraction.

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, 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, 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

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.

Links

Table of n, a(n) for n=1..105.

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

Cf. A113011.

Sequence in context: A072223 A246312 A124907 * A020800 A374449 A248261

Adjacent sequences: A181047 A181048 A181049 * A181051 A181052 A181053

Keyword

cons,nonn

Author

Jonathan D. B. Hodgson, Oct 01 2010

Status

approved