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A229923 Decimal expansion of self-generating 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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified July 25 16:03 EDT 2021. Contains 346291 sequences. (Running on oeis4.)