A215637 Number of solutions of square array of integers, choosing one prime from each row and column.

1, 1, 1, 2, 7, 72, 2144, 2641, 1345721, 2191254096

Offset: 1

Author

Jud McCranie, Aug 18 2012

Keywords

• nonn
• more
• hard

Comments

Let p be the n-th prime number. Put 1 to p^2 into a square array in order. Choose a set of primes such that there is one and only one in each row and column. This is equivalent to non-attacking rooks on prime-numbered squares. Then a(n) is the number of solutions for the n-th prime.

Examples

			For n=2, p=3, and the only solution is {3,5,7}, so a(2) = 1.
		

References

• Martin Erickson, Beautiful Mathematics, Mathematical Association of America, 2011, p. 6. The problem is called Transversal of primes.

Links

• J. K. Andersen, W. Edwin Clark, Jud McCranie, Carlos Rivera, Emmanuel Vantieghem, Puzzle 649 (www.primepuzzles.net)

Crossrefs

Cf. A000217, A000040.