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A245975 Decimal expansion of the number whose continued fraction is the (2,1)-version of the infinite Fibonacci word A014675. 4
2, 7, 0, 2, 9, 3, 8, 3, 5, 8, 0, 2, 2, 5, 1, 0, 2, 9, 4, 4, 4, 5, 0, 5, 0, 9, 7, 4, 6, 9, 3, 0, 0, 3, 7, 3, 4, 5, 3, 2, 7, 0, 3, 1, 5, 2, 9, 0, 9, 2, 3, 1, 2, 2, 1, 4, 0, 1, 4, 1, 2, 0, 0, 0, 3, 0, 7, 7, 4, 6, 9, 8, 3, 7, 2, 6, 6, 4, 8, 0, 2, 7, 0, 3, 5, 5 (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,...); see Example.

LINKS

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

EXAMPLE

[2,1,2,2,1,2,1,2,2,...] = 2.702938358022510294445050974693003734532...

MATHEMATICA

z = 300; seqPosition2[list_, seqtofind_] := Last[Last[Position[Partition[list, Length[#], 1], Flatten[{___, #, ___}], 1, 2]]] &[seqtofind]; x = GoldenRatio;  s =  Differences[Table[Floor[n*x], {n, 1, z^2}]];  (* A014675 *)

x1 = N[FromContinuedFraction[s], 100]

r1 = RealDigits[x1, 10]  (* A245975 *)

ans = Join[{s[[p[0] = pos = seqPosition2[s, #] - 1]]}, #] &[{s[[1]]}];

cfs = Table[s = Drop[s, pos - 1]; ans = Join[{s[[p[n] = pos = seqPosition2[s, #] - 1]]}, #] &[ans], {n, z}];

rcf = Last[Map[Reverse, cfs]]  (* A245920 *)

x2 = N[FromContinuedFraction[rcf], z]

r2 = RealDigits[x2, 10] (* A245976 *)

CROSSREFS

Cf. A014675, A245976.

Sequence in context: A152779 A247373 A021041 * A188737 A200680 A260129

Adjacent sequences:  A245972 A245973 A245974 * A245976 A245977 A245978

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling and Peter J. C. Moses, Aug 08 2014

STATUS

approved

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Last modified March 28 19:06 EDT 2017. Contains 284246 sequences.