A229922 Decimal expansion of self-generating continued fraction with first term (1+sqrt(5))/2, the golden ratio.

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

Offset

1,1

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..86.

Example

f(golden ratio) = 2.1186924975742971994687530627614032053987653143179...

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[GoldenRatio, 300]; t1 = Table[c[x, k], {k, 0, z}]; u = N[c[x, z], 120] (* A229922 *)
RealDigits[u]

Crossrefs

Cf. A064845, A064846, A229779.

Sequence in context: A157785 A021476 A291084 * A051428 A176698 A129276

Adjacent sequences: A229919 A229920 A229921 * A229923 A229924 A229925

Keyword

nonn,cons

Author

Clark Kimberling, Oct 03 2013

Status

approved