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

1,4

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.

References

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

Links

Table of n, a(n) for n=1..10.

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

Example

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

Crossrefs

Cf. A000217, A000040.

Sequence in context: A061421 A304192 A141315 * A119811 A319621 A167526

Adjacent sequences: A215634 A215635 A215636 * A215638 A215639 A215640

Keyword

nonn,more,hard

Author

Jud McCranie, Aug 18 2012

Status

approved