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A364663
a(n+1) = a(|n-a(n)*a(n-1)|)+1; a(0) = 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
0,3
COMMENTS
a(-1) can be set to any finite value and it does not affect the sequence.
FORMULA
a(n) ~ (3*n)^(1/3) (conjectured).
EXAMPLE
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.
PROG
(Python)
a=[0];
for n in range(100):
a.append(a[abs(n-a[n]*a[n-1])]+1)
(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);
KEYWORD
nonn
AUTHOR
Rok Cestnik, Aug 01 2023
STATUS
approved