A373813 a(n) is the smallest number of straight lines needed to intersect all points (k, prime(k)) for k = 1..n.

1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15

Offset: 1

Author

Rémy Sigrist and N. J. A. Sloane, Aug 18 2024

Keywords

• nonn

Comments

Dan Asimov asks if the graph is trying to converge to the Cantor (or Devil's Staircase) function. - N. J. A. Sloane, Aug 25 2024

Links

• Max Alekseyev, Table of n, a(n) for n = 1..410
• Max Alekseyev, Sage program for lines covering points, Github, Aug 19 2024
• N. J. A. Sloane, Sketch to illustrate first 11 terms. Solutions (representing points by their X-coordinates): a(5)=2: {1,5}{2,3,4}; a(9)=3: {1,2}{3,5,7,9}{4,6,8}; a(11)=4: {1,5}{2,3,4}{6,7,10}{8,9,11}.
• N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides [Mentions this sequence]

Crossrefs

Cf. A373814 (run lengths), A373810 (same with y(k) = phi(k)), A373811 (similar with y(k) = a(k)), A375499 (same with y(k)=sigma(k)).

See also A376187, A376188, A376190 for single lines.

Extensions

Terms a(19) onward from Max Alekseyev, Aug 18 2024