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%I #30 Aug 18 2023 23:51:10
%S 0,1,1,2,2,1,3,3,2,3,1,4,2,3,3,2,5,4,2,4,3,5,3,4,4,3,6,2,5,3,4,4,3,5,
%T 3,4,5,5,3,4,5,3,4,7,4,6,4,5,4,4,6,4,5,3,5,4,5,5,4,5,4,5,6,7,4,5,6,5,
%U 5,8,2,7,4,6,6,4,6,6,4,7,5,5,6,5,5,6,5,6,5,8,4,7,5,6,6,5,3,7,5,7
%N a(n+1) = a(|n-a(n)^2|) + 1, a(0) = 0.
%H Michael De Vlieger, <a href="/A364197/b364197.txt">Table of n, a(n) for n = 0..10000</a>
%H Rok Cestnik, <a href="/A364197/a364197.pdf">Term-referencing tree for 1000 terms</a>.
%F a(n) ~ (3n)^(1/3) (conjectured).
%e a(1) = a(|0-a(0)^2|)+1 = a(|0-0|)+1 = a(0)+1 = 1.
%e a(2) = a(|1-a(1)^2|)+1 = a(|1-1|)+1 = a(0)+1 = 1.
%e a(3) = a(|2-a(2)^2|)+1 = a(|2-1|)+1 = a(1)+1 = 2.
%e a(4) = a(|3-a(3)^2|)+1 = a(|3-4|)+1 = a(1)+1 = 2.
%e a(5) = a(|4-a(4)^2|)+1 = a(|4-4|)+1 = a(0)+1 = 1.
%t a[0] = 0; a[n_] := a[n] = a[Abs[n - 1 - a[n - 1]^2]] + 1; Array[a, 100, 0] (* _Amiram Eldar_, Jul 13 2023 *)
%o (Python)
%o a = [0]; [a.append(a[abs(n-a[n]**2)]+1) for n in range(100)]
%Y Cf. A364198 (indices of record highs).
%Y Cf. A339929, A340224.
%Y Cf. A281130, A330772, A340134, A002516, A003056, A004001, A005185.
%K nonn
%O 0,4
%A _Rok Cestnik_, Jul 13 2023
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