MathDB

Say that a sequence

a_1

a_2

a_3

a_4

a_5

a_6

a_7

a_8

is cool if * the sequence contains each of the integers 1 through 8 exactly once, and * every pair of consecutive terms in the sequence are relatively prime. In other words,

a_1

and

a_2

are relatively prime,

a_2

and

a_3

are relatively prime,

\ldots

, and

a_7

and

a_8

are relatively prime.
How many cool sequences are there?

Problem Statement