A377214 - OEIS

%I #6 Oct 23 2024 01:14:55

%S 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,

%T 89,109,113,13,17,29,41,53,71,83,103,113,127,137,151,167,17,19,37,59,

%U 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

%N 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.

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

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

%e Triangle starts with:

%e   2, 3;

%e   3, 5, 7;

%e   5, 7, 11, 19, 23;

%e   7, 11, 17, 23, 29, 41, 47;

%e   ...

%e 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.

%Y Cf. A215637.

%K nonn,tabf

%O 1,1

%A _Martin Renner_, Oct 20 2024