A245976 Decimal expansion of the number whose continued fraction is given by A245920 (limit-reverse of an infinite Fibonacci word).

2, 7, 2, 9, 9, 4, 4, 1, 9, 4, 7, 6, 7, 8, 5, 0, 2, 2, 9, 0, 7, 8, 3, 7, 4, 3, 0, 7, 0, 0, 5, 9, 9, 8, 1, 6, 7, 3, 8, 1, 8, 8, 7, 0, 1, 6, 4, 0, 5, 2, 5, 8, 0, 2, 0, 4, 9, 2, 7, 5, 4, 1, 0, 1, 9, 9, 6, 3, 3, 6, 2, 4, 3, 4, 5, 7, 7, 8, 6, 7, 1, 3, 1, 1, 6, 8

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 limit-reverse, A245920, is the sequence (2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1,...), which is the continued fraction for 2.729944...

For the (0,1)-version of the infinite Fibonacci word 0100101001001... (A003849), the decimal expansion is the same except for the first digit. That is 0.729944194... . - Gandhar Joshi, Mar 28 2024

Links

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

Example

[2,1,2,1,2,2,1,2,1,2,...] =  2.72994419476785022907837430700599816738...

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] (* this sequence *)

Crossrefs

Cf. A245920, A245975.

Sequence in context: A278419 A197133 A178206 * A245216 A223149 A222853

Adjacent sequences: A245973 A245974 A245975 * A245977 A245978 A245979

Keyword

nonn,cons

Author

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

Status

approved