A340134 - OEIS

%I #7 Dec 30 2020 03:04:13

%S 0,0,1,1,1,2,1,2,2,2,3,2,3,2,3,3,3,4,3,4,3,4,3,4,4,4,5,4,5,4,5,4,5,4,

%T 5,5,5,6,5,6,5,6,5,6,5,6,5,6,6,6,7,6,7,6,7,6,7,6,7,6,7,6,7,7,7,8,7,8,

%U 7,8,7,8,7,8,7,8,7,8,7,8,8,8,9,8,9,8,9

%N a(n+1) = a(n-2*a(n)) + 1, starting with a(1) = a(2) = 0.

%F a(n) = floor(sqrt(n-1)) + ((-1)^(n+floor(sqrt(n)))-1)/2.

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

%e a(4) = a(3-2*a(3))+1 = a(1)+1 = 1.

%e a(5) = a(4-2*a(4))+1 = a(2)+1 = 1.

%e a(6) = a(5-2*a(5))+1 = a(3)+1 = 2.

%t Table[Floor[Sqrt[n-1]] + ((-1)^(n+Floor[Sqrt[n]])-1)/2,{n,87}] (* _Stefano Spezia_, Dec 29 2020 *)

%o (Python)

%o a = [0, 0]

%o for n in range(1, 1000):

%o     a.append(a[n-2*a[n]]+1)

%Y For a(n+1) = a(n-a(n)) + 1, starting with a(1) = 0, see A003056.

%Y Cf. A339929, A330772, A005206.

%K nonn

%O 1,6

%A _Rok Cestnik_, Dec 29 2020

%E More terms from _Stefano Spezia_, Dec 29 2020