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A216764 The Lambda word generated by Pi - 2.

%I A216764 #35 Feb 28 2017 22:48:56
%S A216764 0,1,2,1,1,3,1,1,1,4,1,1,1,1,5,1,1,1,1,1,6,1,1,1,1,1,1,7,1,1,1,1,1,1,
%T A216764 1,8,1,1,1,1,1,1,1,8,9,8,1,1,1,1,1,1,8,9,8,9,8,1,1,1,1,1,8,9,8,9,8,9,
%U A216764 8,1,1,1,1,8,9,8,9,8,9,8,9,8,1,1,1,8,9,8,9,8,9,8,9,8,9,8,1,1
%N A216764 The Lambda word generated by Pi - 2.
%C A216764 A Lambda word is a symbolic sequence that encodes differences in the sequence i+j*t, where t is irrational, 1 < t < 2. Here, t = Pi - 2.
%C A216764 A Lambda word is an infinite rich word on an infinite alphabet.
%C A216764 First occurrence of k>0: 2, 3, 6, 10, 15, 21, 28, 36, 45, 144, 299, 510, 777, 1100, 1479, ..., . - _Robert G. Wilson v_, Feb 25 2017
%H A216764 Robert G. Wilson v, <a href="/A216764/b216764.txt">Table of n, a(n) for n = 0..1000</a>
%H A216764 N. Carey, <a href="http://dx.doi.org/10.1007/978-3-642-21590-2_4">On a class of locally symmetric sequences, The right infinite word Lambda Theta</a>, in Mathematics and Computation in Music in Lect. Notes in Comp. Sci., Vol. 6726, Springer, (2011), 42-55.
%H A216764 N. Carey, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Carey/carey6.html">Lambda words: A class of rich words defined over an infinite alphabet</a>, Journal of Integer Sequences, Vol. 16 (2013), Article 13.3.4.
%t A216764 t = Pi - 2;
%t A216764 end = 100;
%t A216764 x = Table[Ceiling[n*1/t], {n, 0, end}];
%t A216764 y = Table[Ceiling[n*t], {n, 0, end}];
%t A216764 tot[p_, q_] := Total[Take[x, p + 1]] + (p*q) + Total[Take[y, q + 1]]
%t A216764 row[r_] := Table[tot[n, r], {n, 0, end - 1}]
%t A216764 g = Grid[Table[row[n], {n, 0, IntegerPart[(end - 1)/t]}]];
%t A216764 pos[n_] := Reverse[Position[g, n][[1, Range[2, 3]]] - 1]
%t A216764 d[n_] := (op[m_] := pos[m + 1] - pos[m];
%t A216764   Abs[Total[ContinuedFraction[op[n][[1]]/op[n][[2]]]]])
%t A216764 l = Prepend[Table[d[n], {n, 1, 249}], 0]
%t A216764 (* _Norman Carey_, Sep 16 2012 *)
%Y A216764 Cf. A216763 (lambda word generated by (1+sqrt(5))/2), A216448 (lambda word generated by log(3)/log(2)).
%K A216764 nonn
%O A216764 0,3
%A A216764 _Norman Carey_, Sep 15 2012