A245975 Decimal expansion of the number whose continued fraction is the (2,1)-version of the infinite Fibonacci word A014675.

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

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