A373813 - OEIS

%I #45 Oct 20 2024 23:34:51

%S 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,

%T 9,9,9,9,9,10,10,10,10,11,11,11,12,12,12,12,12,13,13,13,13,13,13,13,

%U 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

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

%C 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

%H Max Alekseyev, <a href="/A373813/b373813.txt">Table of n, a(n) for n = 1..410</a>

%H Max Alekseyev, <a href="https://github.com/maxale/oeis/blob/main/a3738xx_lines_covering_points.sage">Sage program for lines covering points</a>, Github, Aug 19 2024

%H N. J. A. Sloane, <a href="/A373813/a373813.pdf">Sketch to illustrate first 11 terms</a>. 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}.

%H N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=3RAYoaKMckM">A Nasty Surprise in a Sequence and Other OEIS Stories</a>, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/sloane85BD.pdf">Slides</a> [Mentions this sequence]

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

%Y See also A376187, A376188, A376190 for single lines.

%K nonn

%O 1,3

%A _Rémy Sigrist_ and _N. J. A. Sloane_, Aug 18 2024

%E Terms a(19) onward from _Max Alekseyev_, Aug 18 2024