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Number of solutions of square array of integers, choosing one prime from each row and column.
1

%I #24 Feb 01 2015 09:31:58

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

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

%C 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.

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

%H J. K. Andersen, W. Edwin Clark, Jud McCranie, Carlos Rivera, Emmanuel Vantieghem, <a href="http://www.primepuzzles.net/puzzles/puzz_649.htm">Puzzle 649</a> (www.primepuzzles.net)

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

%Y Cf. A000217, A000040.

%K nonn,more,hard

%O 1,4

%A _Jud McCranie_, Aug 18 2012