A373811 - OEIS

%I #82 Oct 20 2024 23:36:39

%S 0,1,1,2,2,2,3,3,3,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,

%T 8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,12,12,

%U 12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,18

%N a(0) = 0. For n > 0, a(n) is the smallest number of straight lines needed to intersect all points (k, a(k)) for 0 <= k < n.

%C The github site of _Arthur O'Dwyer_ has illustrations of many of the small configurations of lines. At his suggestion, I am including his drawings for n = 5, 8, 13, 17, 23, 28, which are just before a(n) increases.

%D Dominic McCarty, Email to N. J. A. Sloane, Aug 13 2024.

%H Max Alekseyev, <a href="/A373811/b373811.txt">Table of n, a(n) for n = 0..400</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 Dominic McCarty, <a href="/A373811/a373811.txt">Equations entailing a(0) to a(31)</a>

%H Daniel Mondot, <a href="/A373811/a373811_1.txt">Upper bounds on a(n) for n < 10000</a>

%H Arthur O'Dwyer, <a href="https://github.com/Quuxplusone/RecreationalMath/tree/master/A373811">A373811</a>, Github. Includes Python program and many illustrations.

%H Arthur O'Dwyer, <a href="/A373811/a373811.png">Illustration for a(5)</a>

%H Arthur O'Dwyer, <a href="/A373811/a373811_1.png">Illustration for a(8)</a>

%H Arthur O'Dwyer, <a href="/A373811/a373811_2.png">Illustration for a(13)</a>

%H Arthur O'Dwyer, <a href="/A373811/a373811_3.png">Illustration for a(17)</a>

%H Arthur O'Dwyer, <a href="/A373811/a373811_4.png">Illustration for a(23)</a>

%H Arthur O'Dwyer, <a href="/A373811/a373811_5.png">Illustration for a(28)</a>

%H N. J. A. Sloane, <a href="/A373811/a373811.pdf">Sketch illustrating a(8) = 3</a>

%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 See A373812 for the lengths of runs of identical terms.

%Y For minimal sets of lines covering some classic sequences, see A373810, A373813, A375499.

%K nonn,nice

%O 0,4

%A _N. J. A. Sloane_, Aug 13 2024, based on an email from _Dominic McCarty_.

%E a(32)-a(46) from _Zachary DeStefano_, Aug 14 2024

%E a(35) corrected and terms a(47) onward added by _Max Alekseyev_, Aug 15 2024