A368811 a(n) = period length of the sequence A020639(n^k - 1), k >= 1.

1, 1, 1, 1, 1, 2, 1, 1, 1, 12, 1, 10, 1, 1, 1, 60, 1, 10, 1, 1, 1, 18, 1, 2, 1, 1, 1, 660, 1, 66, 1, 1, 1, 1, 1, 10, 1, 1, 1, 4620, 1, 6, 1, 1, 1, 660, 1, 2, 1, 1, 1, 31878, 1, 2, 1, 1, 1, 197340, 1, 5742, 1, 1, 1, 1, 1, 52026, 1, 1, 1, 440220, 1, 28014, 1, 1, 1, 4, 1, 2610, 1, 1, 1, 28014, 1, 2, 1, 1, 1, 3693690, 1, 2, 1, 1, 1, 1, 1, 7590, 1, 1, 1, 1642460820

Offset: 3

Author

Max Alekseyev, Jan 06 2024

Keywords

• nonn

Comments

For n = 2, the sequence A020639(n^k - 1) is not periodic (see A049479), but it is such for any n >= 3.

a(n) divides A058254(A000720(A020639(n-1))).

Examples

			a(8) = 2 is the period length of A010705.
a(12) = 12 is the period length of A366717.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A010705, A020639, A049479, A058254, A366717.

Programs

PARI

{ a368811(n) = my(r=[], z); forprime(p=2, factor(n-1)[1, 1], if(n%p==0, next); z=znorder(Mod(n, p)); if(!#r || vecmin(apply(x->z%x,r)), r=concat(r,[z])) ); lcm(r); }

Formula

For odd n >= 3, a(n) = 1.