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

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

Author

Rok Cestnik, Aug 01 2023

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A364197, A340224, A339929.

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

Programs

PARI

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);

Python

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

Formula

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