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

1,6

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.

Links

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

Example

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

Prog

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

Crossrefs

Cf. A067565.

Sequence in context: A115862 A296030 A270144 * A029357 A118054 A322019

Adjacent sequences: A255977 A255978 A255979 * A255981 A255982 A255983

Keyword

nonn

Author

Peter Kagey, Mar 12 2015

Status

approved