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

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, 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, 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

Offset: 0

Author

Norman Carey and Robert G. Wilson v, Mar 20 2014

Keywords

• nonn

Comments

A Lambda word is a symbolic sequence that encodes differences in the sequence i+j*t, where t is irrational, 1 < t < 2.

First occurrence of k>0: 1, 2, 5, 11, 19, 51, 119, 303, 571, 923, 1359, 4427, 10544, ..., .

Links

• Norman Carey and Robert G. Wilson v, Table of n, a(n) for n = 0..1024
• N. Carey, On a class of locally symmetric sequences, The right infinite word Lambda Theta, in Mathematics and Computation in Music in Lect. Notes in Comp. Sci., Vol. 6726, Springer, (2011), 42-55.
• N. Carey, Lambda words: A class of rich words defined over an infinite alphabet, Journal of Integer Sequences, Vol. 16 (2013), Article 13.3.4.

Crossrefs

Cf. A216448, A216763, A216764.

Programs

Mathematica

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]