A371216 - OEIS

%I #14 Mar 15 2024 23:13:33

%S 1,1,2,3,5,4,5,5,6,7,7,8,8,12,9,10,14,12,13,13,14,15,17,16,17,17,18,

%T 19,19,20,20,30,21,22,32,24,25,25,26,27,29,28,29,29,30,31,31,32,32,48,

%U 33,34,50,36,37,37,38,39,41,40,41,41,42,43,43,44,44,66,45,46,68

%N a(0) = 1, a(1) = 1; for n >= 2, a(n) = Min(a(n - 1), a(n - 2)) + GCD(a(n - 1), n - 1).

%C The plots of a(n) and a(n) - a(n-1) are interesting. Empirically 2*n/3 <= a(n) <= (n-1) and 2/3 <= a(n)/a(n-1) <= 3/2.

%e a(0) = 1;

%e a(1) = 1;

%e a(2) = Min(1, 1) + GCD(1, 1) = 2;

%e a(3) = Min(2, 1) + GCD(2, 2) = 3;

%e a(4) = Min(3, 2) + GCD(3, 3) = 5;

%e and so on.

%t a[0] = a[1] = 1; a[n_] := a[n] = Min[a[n - 1], a[n - 2]] + GCD[a[n - 1], n - 1]; Array[a, 100, 0] (* _Amiram Eldar_, Mar 15 2024 *)

%Y Cf. A364918.

%K nonn

%O 0,3

%A _Ctibor O. Zizka_, Mar 15 2024