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A181050 Decimal expansion of the constant 1+3/(5+7/(9+11/(13+...))), using all odd integers in this generalized continued fraction. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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 A248261 A264991

Adjacent sequences:  A181047 A181048 A181049 * A181051 A181052 A181053

KEYWORD

cons,nonn

AUTHOR

Jonathan D. B. Hodgson, Oct 01 2010

STATUS

approved

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Last modified November 19 10:44 EST 2017. Contains 294936 sequences.