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A055748 A chaotic cousin of the Hofstadter-Conway sequence A004001.

%I A055748 #41 Oct 29 2023 18:03:43
%S A055748 1,1,2,2,2,3,4,4,4,4,5,6,7,8,8,8,8,8,8,9,10,10,10,11,13,15,15,14,15,
%T A055748 16,16,16,16,16,16,16,17,18,18,18,18,18,19,21,23,21,20,24,25,26,28,27,
%U A055748 26,30,30,29,30,30,30,31,32,32,32,32,32,32,32,32,32,33
%N A055748 A chaotic cousin of the Hofstadter-Conway sequence A004001.
%C A055748 See FORMULA for definition.
%D A055748 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 129.
%H A055748 Martin Møller Skarbiniks Pedersen, <a href="/A055748/b055748.txt">Table of n, a(n) for n = 1..10000</a>
%H A055748 J. Grytczuk, <a href="http://dx.doi.org/10.1016/j.disc.2003.10.022">Another variation on Conway's recursive sequence</a>, Discr. Math. 282 (2004), 149-161.
%H A055748 Martin Møller Skarbiniks Pedersen, <a href="/A055748/a055748.pdf">Plot of first 100000000 values (pdf)</a>
%H A055748 Martin Møller Skarbiniks Pedersen, <a href="/A055748/a055748_1.pdf">Plot of a(n)/n for the first 100000000 values (pdf)</a>
%H A055748 Martin Møller Skarbiniks Pedersen, <a href="/A055748/a055748.png">Plot of a(n) for the first 100,000,000 values (png)</a>
%H A055748 Martin Møller Skarbiniks Pedersen, <a href="/A055748/a055748_1.png">Plot of a(n)/n for the first 100000000 values (png)</a>
%H A055748 K. Pinn, <a href="http://projecteuclid.org/euclid.em/1046889590">A chaotic cousin of Conway's recursive sequence</a>, Experimental Mathematics, 9:1 (2000), 55-65.
%H A055748 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%F A055748 a(1) = 1, a(2) = 1, a(n) = a(a(n-1)) + a(n - a(n-2) - 1) for n >= 3. [_Jaroslav Krizek_, Dec 09 2009]
%p A055748 A055748 := proc(n) option remember; if n<=2 then 1 else A055748(A055748(n-1))+A055748(n-1-A055748(n-2)); fi; end;
%t A055748 a[n_] := a[n] = If[n < 3, 1, a[a[n - 1]] + a[n - a[n - 2] - 1]]; Array[a, 70] (* _Michael De Vlieger_, Mar 29 2017 *)
%Y A055748 Cf. A004001, A005185.
%K A055748 nonn,look
%O A055748 1,3
%A A055748 _N. J. A. Sloane_, Jul 13 2000