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A245975
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Decimal expansion of the number whose continued fraction is the (2,1)-version of the infinite Fibonacci word A014675.
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4
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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[2,1,2,2,1,2,1,2,2,...] = 2.702938358022510294445050974693003734532...
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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