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staircase like effect in a chaotic sequence

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  • Roger Bagula
    I captured the step like entropy into an integer sequence with this one. %I A167383 %S A167383
    Message 1 of 1 , Nov 2, 2009
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      I captured the step like entropy into
      an integer sequence with this one.


      %I A167383
      %S A167383 0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,5,
      %T A167383 5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,8,9,9,9,10,10,11,11,11,11,11,11,12,13,13,
      %U A167383 14,15,15,15,16,16,16,17,17,18,18,19,19,19,19,20,20,20,21,21,21,21,22
      %N A167383 Entropy like stair step sequence based on A008185: a(n)=a(n-1)+Ceiling[-(A008185[n + 2]/A008185[n + 1])*Log[(A008185[n + 2]/A008185[n + 1])]/Log[2]]
      %C A167383 By using the ratio:
      %C A167383 A008185[n + 2]/A008185[n + 1]
      %C A167383 the sequence gets a probability effect that gives
      %C A167383 a devil's staircase like result.
      %F A167383 a(n)=a(n-1)+Ceiling[-(A008185[n + 2]/A008185[n + 1])*Log[(A008185[n + 2]/A008185[n + 1])]/Log[2]]
      %t A167383 Clear[f, g, n]; f[0] = 1; f[1] = 1; f[2] = 1;
      %t A167383 f[n_] := f[n] = f[n - f[n - 1]] + f[n - f[n - 2]];
      %t A167383 g[0] = 0; g[1] = 1;
      %t A167383 g[n_] := g[n] = g[n - 1] + Ceiling[-(f[n + 2]/f[n + 1])*Log[(f[n + 2]/f[n + 1])]/Log[2]]
      %t A167383 a = Table[g[n], {n, 0, 200}]
      %Y A167383 A008185,A136640
      %K A167383 nonn
      %O A167383 0,15
      %A A167383 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 02 2009




      --
      Respectfully, Roger L. Bagula
      11759 Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
      http://www.google.com/profiles/Roger.Bagula
      alternative email: roger.bagula@...
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