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

1,1

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

Links

Table of n, a(n) for n=1..45.

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

Example

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.

Crossrefs

Cf. A376187, A376188.

Sequence in context: A055937 A090255 A228162 * A080669 A099205 A051005

Adjacent sequences: A376187 A376188 A376189 * A376191 A376192 A376193

Keyword

nonn,more

Author

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

Extensions

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

Status

approved