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

1,7

Comments

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

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

Links

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

Formula

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

Example

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.

Prog

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

Crossrefs

Cf. A001146, A007733, A002326.

First differs from A256608 at n=43.

Column 2 of triangle in A279185.

Sequence in context: A363320 A351032 A280726 * A256608 A279186 A164799

Adjacent sequences: A256604 A256605 A256606 * A256608 A256609 A256610

Keyword

nonn

Author

Ivan Neretin, Apr 04 2015

Status

approved