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A239507 The Lambda word generated by E-1 (A091131).

%I A239507 #12 Apr 25 2025 20:40:58
%S A239507 0,1,2,1,2,3,2,2,3,2,2,4,2,2,2,4,2,2,4,5,4,2,2,4,5,4,2,4,5,4,5,4,2,4,
%T A239507 5,4,5,4,4,5,4,5,4,5,4,4,5,4,5,4,5,6,5,4,5,4,5,4,5,6,5,4,5,4,5,6,5,5,
%U A239507 6,5,4,5,4,5,6,5,5,6,5,4,5,6,5,5,6,5,5,6,5,4,5,6,5,5,6,5,5,6,5,6,5,5,6,5,5,6,5,5,6,5,6,5
%N A239507 The Lambda word generated by E-1 (A091131).
%C A239507 A Lambda word is a symbolic sequence that encodes differences in the sequence i+j*t, where t is irrational, 1 < t < 2.
%C A239507 First occurrence of k>0: 1, 2, 5, 11, 19, 51, 119, 303, 571, 923, 1359, 4427, 10544, ..., .
%H A239507 Norman Carey and Robert G. Wilson v, <a href="/A239507/b239507.txt">Table of n, a(n) for n = 0..1024</a>
%H A239507 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 A239507 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 A239507 t = E - 1; mx = 20; x = Table[ Ceiling[n*1/t], {n, 0, mx}]; y = Table[ Ceiling[n*t], {n, 0, mx}]; tot[p_, q_] := Total[ Take[x, p + 1]] + (p*q) + Total[ Take[y, q + 1]]; row[r_] := Table[ tot[n, r], {n, 0, mx - 1}]; g = Grid[ Table[ row[n], {n, 0, IntegerPart[(mx - 1)/t]}]]; pos[n_] := Reverse[ Position[ g, n][[1, Range[2, 3]]] - 1]; d[n_] := (d[0] = 0; op[m_] := pos[m + 1] - pos[m]; Abs[ Total[ ContinuedFraction[ op[n][[1]] / op[n][[2]] ]]]); lst = Prepend[ Table[ d[n], {n, 0, 249}], 0]
%Y A239507 Cf. A216448, A216763, A216764.
%K A239507 nonn
%O A239507 0,3
%A A239507 _Norman Carey_ and _Robert G. Wilson v_, Mar 20 2014