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

1,2

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.

Links

Table of n, a(n) for n=1..15.

Situ Zhengmei, Prime ring, Chinese Math Blog.

Formula

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

Example

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].

Crossrefs

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

Sequence in context: A067700 A270554 A037010 * A114695 A134084 A267346

Adjacent sequences: A294181 A294182 A294183 * A294185 A294186 A294187

Keyword

nonn,more

Author

Michel Marcus, Feb 11 2018

Extensions

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

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

Status

approved