A376190 For a line L in the plane, let C(L) denote the number of prime points [k, prime(k)] on L, and let M(L) denote the maximum prime(k) for any of these points. a(n) is the maximum of the smallest primes in the lines L with C(L) = n and containing prime A376187(n), or a(n) = -1 if no such lines exist.

2, 2, 3, 5, 19, 18, 7, 13, 967, 113, 83, 619, 103, 1583, 1693, 1621, 1759, 1753, 5923, 197, 6143, 15823, 5849, 1609, 1663, 10333, 1613, 152003, 15683, 16111, 1619, 141871, 15649, 15383, 140989, 141811, 136481, 141319, 15667, 136769, 16033, 16619, 141707, 15473, 135649

Offset: 1

Author

N. J. A. Sloane, Sep 25 2024, following a suggestion from W. Edwin Clark

Keywords

• nonn
• more

Comments

Consider all the lines L in the plane containing exactly n prime-points (k, prime(k)). A376187 minimizes the maximal prime on any such line L, while the present sequence then maximizes the minimal prime on the lines from A376187.

In other words, we first minimize (in A376187) the maximal prime over all lines with exactly n points, and then here we further maximize the minimal prime. The second step minimizes the spread of the points.

For most listed terms, there is only one line L with C(L) = n that contains prime A376187(n). - Max Alekseyev, Sep 28 2024

Examples

			The best line with 5 points contains the primes 19,23,31,43,47, so a(5) = 19 and A376187(5) = 47. See the Table for further examples.
		

Links

• N. J. A. Sloane, Table of lines in the plane containing the known maximum numbers of prime-points

Crossrefs

Cf. A376187, A376188.

Extensions

Better definition and a(28)-a(45) from Max Alekseyev, Sep 28 2024