

A229923


Decimal expansion of selfgenerating continued fraction with first term sqrt(2).


1



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

1,2


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..105.


EXAMPLE

f(sqrt(2)) = 1.967552445870374625939484944608025225084419714910878...


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[Sqrt[2], 300]; t1 = Table[c[x, k], {k, 0, z}]; u = N[c[x, z], 120] (* A229923 *)
RealDigits[u]


CROSSREFS

Cf. A064845, A064846, A229779.
Sequence in context: A254980 A318336 A340577 * A203080 A197375 A019643
Adjacent sequences: A229920 A229921 A229922 * A229924 A229925 A229926


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Oct 03 2013


EXTENSIONS

More terms from and example corrected by Rick L. Shepherd, Jan 24 2014


STATUS

approved



