A339310 - OEIS

%I #30 Dec 19 2020 07:49:21

%S 1,1,2,3,3,3,5,4,6,5,6,8,8,6,9,8,8,11,11,10,10,14,12,11,16,15,12,17,

%T 14,17,16,18,14,19,19,16,21,22,19,21,25,18,22,25,23,24,25,25,23,31,28,

%U 22,33,28,29,32,28,29,30,30,33,35,29,33,32,28,41,36,35

%N a(n) = a(n-1-a(n-1)) + a(n-a(n-2)) for n>2; starting with a(1) = a(2) = 1.

%C {a(n)} is the Pinn F 1,0(n) sequence (see link section).

%H K. Pinn, <a href="https://arxiv.org/abs/cond-mat/9808031v1">A Chaotic Cousin Of Conway's Recursive Sequence</a>, arXiv:cond-mat/9808031 [cond-mat.stat-mech], 1998.

%e a(3)=2 because a(3) = a(3-1-a(3-1))+a(3-a(3-2)) = a(2-1)+a(3-1) = 1+1 = 2.

%t a[1] = a[2] = 1; a[n_] := a[n] = a[n - 1 - a[n - 1]] + a[n - a[n - 2]]; Table[ a[n], {n, 1, 40}]

%o (Python3)

%o a=[1,1]

%o for n in range(100):

%o     i1=len(a)-1-a[len(a)-1]

%o     i2=len(a)-a[len(a)-2]

%o     if i1>=0 and i2>=0 :

%o         a.append(a[i1]+a[i2])

%o     else :

%o         print("Sequence dies. Contains ", n+2, " terms.")

%o         break

%o print(a)

%o (PARI) lista(nn) = {my(va = vector(nn)); va[1] = 1; va[2] = 1; for (n=3, nn, va[n]=va[n-1-va[n-1]]+va[n-va[n-2]];); va;} \\ _Michel Marcus_, Dec 07 2020

%Y Cf. A005185, A070867, A046699.

%K nonn

%O 1,3

%A _Pablo Hueso Merino_, Dec 02 2020