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

%I A373813 #49 Feb 15 2025 01:56:19
%S A373813 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 A373813 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 A373813 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 A373813 a(n) is the smallest number of straight lines needed to intersect all points (k, prime(k)) for k = 1..n.
%C A373813 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 A373813 Max Alekseyev, <a href="/A373813/b373813.txt">Table of n, a(n) for n = 1..410</a>
%H A373813 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 A373813 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 A373813 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 A373813 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)).
%Y A373813 See also A376187, A376188, A376190 for single lines.
%K A373813 nonn
%O A373813 1,3
%A A373813 _Rémy Sigrist_ and _N. J. A. Sloane_, Aug 18 2024
%E A373813 Terms a(19) onward from _Max Alekseyev_, Aug 18 2024