A255980 Number of iterations of A067565 required to reach a perfect square.

0, 1, 1, 0, 1, 2, 1, 2, 0, 2, 1, 3, 1, 2, 3, 0, 1, 3, 1, 4, 3, 2, 1, 4, 0, 2, 4, 4, 1, 5, 1, 5, 3, 2, 5, 0, 1, 2, 3, 5, 1, 6, 1, 4, 6, 2, 1, 6, 0, 6, 3, 4, 1, 7, 5, 7, 3, 2, 1, 7, 1, 2, 7, 0, 5, 6, 1, 4, 3, 8, 1, 8, 1, 2, 8, 4, 8, 6, 1, 7, 0, 2, 1, 9, 5, 2, 3

Offset: 1

Author

Peter Kagey, Mar 12 2015

Keywords

• nonn

Comments

Iterating A067565 will always result in a perfect square, because all fixed points are squares, and A067565(n) <= n all n.

a(n) = 0 if and only if n is a perfect square.

a(n) = 1 if and only if n is prime.

Examples

			Let g(n) = A067565(n)
a(12) = 3 because g(g(g(12))) = g(g(6)) = g(3) = 0, which is a perfect square.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A067565.

Programs

Ruby

def a(n)
  c = 0
  n = a067565(n) while n.is_nonsquare? && c += 1
  c
end