A340224 -id:A340224 - cp's OEIS frontend

A364197 a(n+1) = a(|n-a(n)^2|) + 1, a(0) = 0.

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, 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, 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

Offset: 0

Rok Cestnik, Jul 13 2023

nonn

			a(1) = a(|0-a(0)^2|)+1 = a(|0-0|)+1 = a(0)+1 = 1.
a(2) = a(|1-a(1)^2|)+1 = a(|1-1|)+1 = a(0)+1 = 1.
a(3) = a(|2-a(2)^2|)+1 = a(|2-1|)+1 = a(1)+1 = 2.
a(4) = a(|3-a(3)^2|)+1 = a(|3-4|)+1 = a(1)+1 = 2.
a(5) = a(|4-a(4)^2|)+1 = a(|4-4|)+1 = a(0)+1 = 1.

Michael De Vlieger, Table of n, a(n) for n = 0..10000
Rok Cestnik, Term-referencing tree for 1000 terms.

Cf. A364198 (indices of record highs).
Cf. A339929, A340224.
Cf. A281130, A330772, A340134, A002516, A003056, A004001, A005185.

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 *)

a = [0]; [a.append(a[abs(n-a[n]**2)]+1) for n in range(100)]

a(n) ~ (3n)^(1/3) (conjectured).

A364663 a(n+1) = a(|n-a(n)*a(n-1)|)+1; a(0) = 0.

Original entry on oeis.org

0, 1, 2, 1, 2, 3, 2, 1, 4, 3, 2, 3, 4, 1, 4, 3, 2, 3, 4, 3, 2, 5, 4, 3, 4, 5, 4, 3, 4, 3, 4, 5, 4, 5, 2, 5, 6, 3, 4, 5, 4, 3, 4, 5, 4, 5, 6, 3, 4, 7, 6, 5, 6, 5, 4, 3, 6, 5, 4, 5, 6, 5, 6, 5, 6, 3, 4, 5, 4, 5, 8, 5, 6, 5, 6, 5, 6, 7, 6, 7, 4, 7, 6, 5, 6, 5, 4, 5, 6, 5, 6, 7, 8, 7, 4, 5, 6

Offset: 0

Rok Cestnik, Aug 01 2023

nonn

a(-1) can be set to any finite value and it does not affect the sequence.

			a(1) = a(|0-a(0)*____|)+1 = a(0)+1 = 1.
a(2) = a(|1-a(1)*a(0)|)+1 = a(1)+1 = 2.
a(3) = a(|2-a(2)*a(1)|)+1 = a(0)+1 = 1.

Cf. A364197, A340224, A339929.

Cf. A005185, A004001, A003056, A340134, A007660.

N=100; a=vector(N); a[2]=1; for(n=1,N-2,a[n+2]=a[1+abs(n-a[n]*a[n+1])]+1);

a=[0];
for n in range(100):
    a.append(a[abs(n-a[n]*a[n-1])]+1)

a(n) ~ (3*n)^(1/3) (conjectured).

cp's OEIS Frontend

A364197 a(n+1) = a(|n-a(n)^2|) + 1, a(0) = 0.

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