|
%I #10 Aug 21 2014 17:55:40
%S 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,
%T 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,
%U 4,6,9,8,3,7,2,6,6,4,8,0,2,7,0,3,5,5
%N Decimal expansion of the number whose continued fraction is the (2,1)-version of the infinite Fibonacci word A014675.
%C 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.
%e [2,1,2,2,1,2,1,2,2,...] = 2.702938358022510294445050974693003734532...
%t 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 *)
%t x1 = N[FromContinuedFraction[s], 100]
%t r1 = RealDigits[x1, 10] (* A245975 *)
%t ans = Join[{s[[p[0] = pos = seqPosition2[s, #] - 1]]}, #] &[{s[[1]]}];
%t cfs = Table[s = Drop[s, pos - 1]; ans = Join[{s[[p[n] = pos = seqPosition2[s, #] - 1]]}, #] &[ans], {n, z}];
%t rcf = Last[Map[Reverse, cfs]] (* A245920 *)
%t x2 = N[FromContinuedFraction[rcf], z]
%t r2 = RealDigits[x2, 10] (* A245976 *)
%Y Cf. A014675, A245976.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_ and _Peter J. C. Moses_, Aug 08 2014
|
