A377214 Irregular triangle T(n, k), read by rows with 1 <= k <= p = A000040(n), for the very first solution to the transversal of primes problem.

2, 3, 3, 5, 7, 5, 7, 11, 19, 23, 7, 11, 17, 23, 29, 41, 47, 11, 13, 29, 41, 53, 59, 71, 83, 89, 109, 113, 13, 17, 29, 41, 53, 71, 83, 103, 113, 127, 137, 151, 167, 17, 19, 37, 59, 73, 89, 103, 131, 151, 167, 179, 197, 211, 227, 251, 271, 283, 19, 23, 41, 59, 83, 107, 127, 139, 157, 181, 191, 227, 239, 263, 281, 293, 313, 337, 359

Offset: 1

Author

Martin Renner, Oct 20 2024

Keywords

• nonn
• tabf

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. Then T(n, k) gives the first of solutions for the n-th prime according to the size of the selected prime numbers.

Examples

			Triangle starts with:
  2, 3;
  3, 5, 7;
  5, 7, 11, 19, 23;
  7, 11, 17, 23, 29, 41, 47;
  ...
For n = 4, p = 7 there are two solutions {7, 11, 17, 23, 29, 41, 47} and {7, 11, 19, 23, 31, 41, 43}, the first of which is listed in the table.
		

References

• Martin Erickson, Beautiful Mathematics, Mathematical Association of America, 2011, p. 6 (Transversal of primes).

Crossrefs

Cf. A215637.