A373811 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.

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, 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, 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

Offset: 0

Author

N. J. A. Sloane, Aug 13 2024, based on an email from Dominic McCarty

Keywords

• nonn
• nice

Comments

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.

References

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

Links

• Max Alekseyev, Table of n, a(n) for n = 0..400
• Max Alekseyev, Sage program for lines covering points, Github, Aug 19 2024
• Dominic McCarty, Equations entailing a(0) to a(31)
• Daniel Mondot, Upper bounds on a(n) for n < 10000
• Arthur O'Dwyer, A373811, Github. Includes Python program and many illustrations.
• Arthur O'Dwyer, Illustration for a(5)
• Arthur O'Dwyer, Illustration for a(8)
• Arthur O'Dwyer, Illustration for a(13)
• Arthur O'Dwyer, Illustration for a(17)
• Arthur O'Dwyer, Illustration for a(23)
• Arthur O'Dwyer, Illustration for a(28)
• N. J. A. Sloane, Sketch illustrating a(8) = 3
• 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

See A373812 for the lengths of runs of identical terms.

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

Extensions

a(32)-a(46) from Zachary DeStefano, Aug 14 2024

a(35) corrected and terms a(47) onward added by Max Alekseyev, Aug 15 2024