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A246129 Decimal expansion of the number whose continued fraction is given by A246127 (limiting block extension of an infinite Fibonacci word). 3
2, 3, 6, 6, 3, 0, 4, 6, 9, 4, 6, 5, 3, 2, 7, 2, 6, 5, 6, 6, 8, 2, 4, 9, 7, 2, 0, 5, 8, 6, 1, 4, 5, 6, 9, 1, 0, 0, 8, 1, 9, 9, 4, 8, 1, 0, 4, 0, 9, 5, 8, 9, 1, 0, 9, 3, 0, 5, 4, 1, 0, 2, 7, 1, 3, 8, 5, 3, 7, 7, 9, 1, 0, 1, 9, 1, 3, 5, 3, 1, 1, 3, 4, 6, 2, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The (2,1)-version of the infinite Fibonacci word, A014675, as a sequence, is (2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2,...).  Its limiting block extension, A246128, is the sequence (2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2,...), which is the continued fraction for 2.366304...

LINKS

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

EXAMPLE

[2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1,...] =  2.3663046946532726566824972058...

MATHEMATICA

seqPosition1[list_, seqtofind_] := If[Length[#] > Length[list], {}, Last[Last[      Position[Partition[list, Length[#], 1], Flatten[{___, #, ___}], 1, 1]]]] &[seqtofind]; s = Differences[Table[Floor[n*GoldenRatio], {n, 10000}]]; t = {{2}}; p[0] = seqPosition1[s, Last[t]]; s = Drop[s, p[0]]; Off[Last::nolast]; n = 1; While[(p[n] = seqPosition1[s, Last[t]]) > 0, (AppendTo[t, Take[s, {#, # + Length[Last[t]]}]]; s = Drop[s, #]) &[p[n]]; n++]; On[Last::nolast]; t1 = Last[t] (*A246127*)

q = -1 + Accumulate[Table[p[k], {k, 0, n - 1}]] (*A246128*)

u = N[FromContinuedFraction[t1], 100]

r = RealDigits[u][[1]] (* A246129 *)

CROSSREFS

Cf. A246127, A246128, A014675, A245975.

Sequence in context: A333304 A248896 A102402 * A124498 A197334 A113399

Adjacent sequences:  A246126 A246127 A246128 * A246130 A246131 A246132

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling and Peter J. C. Moses, Aug 15 2014

STATUS

approved

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Last modified May 26 09:37 EDT 2020. Contains 334620 sequences. (Running on oeis4.)