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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)