This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A375423 #15 Aug 17 2024 12:21:05
%S A375423 1,1,2,2,2,3,3,3,3,4,4,4,3,5,5,4,4,5,3,6,4,6,3,7,5,4,7,4,8,4,9,5,5,6,
%T A375423 4,10,6,4,11,6,5,7,3,8,3,9,4,12,3,10,4,13,3,11,5,8,3,12,6,6,7,4,14,4,
%U A375423 15,4,16,4,17,4,18,5,9,4,19,4,20,5,10,3,13,3
%N A375423 a(1) = 1; for any n > 1, a(n) is the maximum number of points from the set {(k, a(k)), k = 1..n-1} belonging to a straight line passing through the point (n-1, a(n-1)).
%C A375423 This sequence is unbounded (if the sequence was bounded, say by m, then, by the pigeonhole principle, some value v <= m would appear infinitely many times, and for any k > 0, the k-th occurrence of v would be followed by a value >= k, a contradiction).
%H A375423 Rémy Sigrist, <a href="/A375423/b375423.txt">Table of n, a(n) for n = 1..10000</a>
%H A375423 Rémy Sigrist, <a href="/A375423/a375423_1.txt">C++ program</a>
%H A375423 Rémy Sigrist, <a href="/A375423/a375423.gp.txt">PARI program</a>
%e A375423 The first terms, alongside an appropriate set of points, are:
%e A375423 n a(n) Points
%e A375423 -- ---- -----------------------------------
%e A375423 1 1 N/A
%e A375423 2 1 (1,1)
%e A375423 3 2 (1,1), (2,1)
%e A375423 4 2 (1,1), (3,2)
%e A375423 5 2 (1,1), (4,2)
%e A375423 6 3 (3,2), (4,2), (5,2)
%e A375423 7 3 (2,1), (4,2), (6,3)
%e A375423 8 3 (1,1), (4,2), (7,3)
%e A375423 9 3 (2,1), (5,2), (8,3)
%e A375423 10 4 (6,3), (7,3), (8,3), (9,3)
%e A375423 11 4 (1,1), (4,2), (7,3), (10,4)
%e A375423 12 4 (2,1), (5,2), (8,3), (11,4)
%e A375423 13 3 (4,2), (8,3), (12,4)
%e A375423 14 5 (6,3), (7,3), (8,3), (9,3), (13,3)
%e A375423 15 5 (2,1), (5,2), (8,3), (11,4), (14,5)
%o A375423 (C++) // See Links section.
%o A375423 (PARI) \\ See Links section.
%Y A375423 Cf. A334043, A375422.
%K A375423 nonn
%O A375423 1,3
%A A375423 _Rémy Sigrist_, Aug 14 2024