

A229920


Decimal expansion of selfgenerating continued fraction with first term 2.


4



2, 4, 2, 5, 6, 0, 1, 4, 4, 0, 2, 7, 7, 1, 4, 5, 3, 9, 9, 9, 3, 8, 3, 2, 6, 2, 1, 7, 7, 0, 1, 2, 6, 2, 6, 0, 6, 4, 8, 4, 7, 4, 6, 5, 3, 2, 9, 5, 1, 1, 6, 9, 4, 3, 7, 7, 9, 2, 3, 3, 2, 9, 0, 1, 6, 3, 9, 2, 2, 6, 9, 9, 2, 1, 5, 8, 6, 1, 8, 6, 5, 8, 9, 7, 0, 3
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OFFSET

1,1


COMMENTS

For x > 0, define c(x,0) = x and c(x,n) = [c(x,0), ..., c(x,n1)]. We call f(x) the selfgenerating continued fraction with first term x. See A229779.


LINKS

Table of n, a(n) for n=1..86.


EXAMPLE

c(x,0) = x, so that c(2,0) = 2;
c(x,1) = [x, x], so that c(2,1) = 5/2;
c(x,2) = [x, x, [x, x]], so that c(2,2) = 29/12;
c(x,3) = [x, x, [x, x], [x, x, [x, x]]], so that c(2,3) = 961/396 = 2.4267...;
c(2,4)= 45667561/45667561/18267036 = 2.42545...;
c(2,5) = 2.454562...;
f(2) = 2.4256014402771453999383262177012626064847465329511694...


MATHEMATICA

$MaxExtraPrecision = Infinity; z = 300; c[x_, 0] := x; c[x_, n_] := c[x, n] = FromContinuedFraction[Table[c[x, k], {k, 0, n  1}]]; x = N[2, 300]; t1 = Table[c[x, k], {k, 0, z}]; u = N[c[x, z], 120] (* A229920 *)
RealDigits[u]


CROSSREFS

Cf. A064845, A064846, A229779.
Sequence in context: A020774 A291303 A347098 * A201562 A190041 A189326
Adjacent sequences: A229917 A229918 A229919 * A229921 A229922 A229923


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Oct 03 2013


STATUS

approved



