login
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.
0
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
1,1
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.
REFERENCES
Martin Erickson, Beautiful Mathematics, Mathematical Association of America, 2011, p. 6 (Transversal of primes).
EXAMPLE
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.
CROSSREFS
Cf. A215637.
Sequence in context: A239586 A180611 A084127 * A089934 A113460 A113470
KEYWORD
nonn,tabf
AUTHOR
Martin Renner, Oct 20 2024
STATUS
approved