A256607 Eventual period of 2^(2^k) mod n.

1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 4, 1, 2, 2, 1, 1, 1, 2, 6, 1, 2, 4, 10, 1, 4, 2, 6, 2, 3, 1, 4, 1, 4, 1, 2, 2, 6, 6, 2, 1, 4, 2, 3, 4, 2, 10, 11, 1, 6, 4, 1, 2, 12, 6, 4, 2, 6, 3, 28, 1, 4, 4, 2, 1, 2, 4, 10, 1, 10, 2, 12, 2, 6, 6, 4, 6, 4, 2, 12, 1, 18, 4, 20, 2, 1, 3

Offset: 1

Author

Ivan Neretin, Apr 04 2015

Keywords

• nonn

Comments

In other words, eventual period of 2 under the map x -> x^2 mod n.

a(n) is a divisor of A256608(n).

Examples

			For n=9 the map acts as follows: 2 -> 4 -> 7 -> 4 -> 7 and so on. This means the eventual period is 2, hence a(9)=2.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001146, A007733, A002326.

First differs from A256608 at n=43.

Column 2 of triangle in A279185.

Programs

Haskell

a256607 = a007733 . fromIntegral . a007733
-- Reinhard Zumkeller, Apr 13 2015

Formula

a(n) = A007733(A007733(n)).