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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.
0
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
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
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