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

0,4

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.

Sequence in context: A246435 A301461 A172471 * A373810 A375433 A046155

Adjacent sequences: A373808 A373809 A373810 * A373812 A373813 A373814

Keyword

nonn,nice,changed

Author

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

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

Status

approved