A229923 Decimal expansion of self-generating continued fraction with first term sqrt(2).

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

Offset

1,2

Comments

For x > 0, define c(x,0) = x and c(x,n) = [c(x,0), ..., c(x,n-1)]. We call f(x) the self-generating 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