A364197 -id:A364197 - cp's OEIS frontend

A364198 Index of first occurrence of n in A364197.

0, 1, 3, 6, 11, 16, 26, 43, 69, 115, 141, 158, 208, 293, 358, 440, 541, 642, 743, 1117, 1378, 1612, 1826, 2052, 2494, 2856, 3181, 3703, 4107, 4862, 5347, 5924, 6454, 7645, 8322, 8999, 9784, 10941, 12458, 13580, 14542, 15839, 16864, 18309, 19876, 21696, 23311, 25408, 28377, 30314

Offset: 0

Rok Cestnik, Jul 13 2023

nonn

Cf. A364197.

s[0] = 0; s[n_] := s[n] = s[Abs[n - 1 - s[n - 1]^2]] + 1; TakeWhile[Flatten[FirstPosition[Array[s, 32000, 0] , #] & /@ Range[0, 50]] - 1 , NumberQ] (* Amiram Eldar, Jul 13 2023 *)

a = [0]; [a.append(a[abs(n-a[n]**2)]+1) for n in range(1000)] # A364197
b = [a.index(n) for n in range(max(a)+1)] # A364198

a(n) ~ n^3/3 (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

A364198 Index of first occurrence of n in A364197.

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