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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.
8
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
1,3
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, 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 (similar with y(k)=a(k)), A373811 (same with y(k) = phi(k)), A375499 (same with y(k)=sigma(k)).
See also A376187, A376188, A376190 for single lines.
Sequence in context: A108229 A023966 A368942 * A088141 A185283 A214972
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(19) onward from Max Alekseyev, Aug 18 2024
STATUS
approved