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A239507
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The Lambda word generated by E-1 (A091131).
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1
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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
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OFFSET
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0,3
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COMMENTS
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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, ..., .
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LINKS
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MATHEMATICA
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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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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