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A255980
Number of iterations of A067565 required to reach a perfect square.
1
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.
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
KEYWORD
nonn
AUTHOR
Peter Kagey, Mar 12 2015
STATUS
approved