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A087721 Strictly increasing domain of the Hofstadter batrachian sequence A005185. 0

%I

%S 2,3,4,5,6,8,10,11,12,16,20,21,22,23,24,25,30,32,38,39,40,41,42,43,44,

%T 45,46,47,48,52,54,56,58,60,61,62,64,66,68,71,72,73,77,78,79,80,82,83,

%U 85,87,88,90,91,92,93,94,96,101,106,108,109,111,114,115,118,120,122,123

%N Strictly increasing domain of the Hofstadter batrachian sequence A005185.

%C This result came from discussion with _Robert G. Wilson v_ about variations in chaotic sequences. The conclusion is that there are three distinct sets: (1) consecutive repeating, (2) strictly increasing and (3) strictly decreasing.

%F a(n) =a(n - a(n-1)) + a(n - a(n-2)).

%t digits=750 Hofstadter[n_Integer?Positive] := Hofstadter[n] = Hofstadter[n - Hofstadter[n-1]] + Hofstadter[n - Hofstadter[n-2]] Hofstadter[1] = Hofstadter[2] = 1 a1=Table[Hofstadter[n], {n, 1, digits}]; f[x_, y_] := x-y/; x-y>0 f[x_, y_] := 0/; x-y<=0 b=Table[If[f[a1[[n]], a1[[n-1]]]>0, a1[[n]], 0], {n, 2, digits}]; c=Delete[Union[b], 1]

%Y Cf. A005185, A087722, A087723.

%K nonn

%O 1,1

%A _Roger L. Bagula_, Sep 29 2003

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Last modified September 25 22:18 EDT 2021. Contains 347664 sequences. (Running on oeis4.)