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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.
3
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
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
Sequence in context: A055937 A090255 A228162 * A080669 A099205 A051005
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