A294184 a(n) is the number of ways to arrange numbers from 1 to 2*n in a row, starting with 1, such that the sum of every two adjacent numbers is prime, but also considering the ends as adjacent.

1, 2, 2, 4, 96, 1024, 2880, 81024, 770144, 6309300, 213812336, 6395634044, 165849732426, 8050337724850, 255709623233382

Offset: 1

Author

Michel Marcus, Feb 11 2018

Keywords

• nonn
• more

Comments

When the size of the row is odd, it is impossible to find such an arrangement, so that sequence is only defined for even-sized rows.

Examples

			a(1) = 1, because of [1, 2].
a(2) = 2, because of [1, 2, 3, 4] and [1, 4, 3, 2].
a(3) = 2, because of [1, 4, 3, 2, 5, 6] and [1, 6, 5, 2, 3, 4].
		

Links

• Situ Zhengmei, Prime ring, Chinese Math Blog.

Crossrefs

Cf. A036440, A051252, A051239, A242527, A242528.

Formula

a(n) = 2*A051252(n), for n > 1. - Giovanni Resta, Feb 25 2020

Extensions

a(9)-a(11) from Jackson Bahm, Feb 25 2020

a(12)-(15) from Giovanni Resta, using A051252, Feb 25 2020