A340134 a(n+1) = a(n-2*a(n)) + 1, starting with a(1) = a(2) = 0.

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, 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, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 8, 8, 9, 8, 9, 8, 9

Offset: 1

Author

Rok Cestnik, Dec 29 2020

Keywords

• nonn

Examples

			a(3) = a(2-2*a(2))+1 = a(2)+1 = 1.
a(4) = a(3-2*a(3))+1 = a(1)+1 = 1.
a(5) = a(4-2*a(4))+1 = a(2)+1 = 1.
a(6) = a(5-2*a(5))+1 = a(3)+1 = 2.
		

Crossrefs

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

Cf. A339929, A330772, A005206.

Programs

Mathematica

Table[Floor[Sqrt[n-1]] + ((-1)^(n+Floor[Sqrt[n]])-1)/2,{n,87}] (* Stefano Spezia, Dec 29 2020 *)

Python

a = [0, 0]
for n in range(1, 1000):
    a.append(a[n-2*a[n]]+1)

Formula

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

Extensions

More terms from Stefano Spezia, Dec 29 2020