A368811 - OEIS

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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

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

OFFSET

3,6

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))).

LINKS

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

FORMULA

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

EXAMPLE

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

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

PROG

(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); }

CROSSREFS

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

Sequence in context: A066017 A236938 A079834 * A342458 A358722 A256688

Adjacent sequences: A368808 A368809 A368810 * A368812 A368813 A368814

KEYWORD

nonn

AUTHOR

Max Alekseyev, Jan 06 2024

STATUS

approved