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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)).
1
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, 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, 15, 4, 16, 4, 17, 4, 18, 5, 9, 4, 19, 4, 20, 5, 10, 3, 13, 3
OFFSET
1,3
COMMENTS
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).
LINKS
Rémy Sigrist, C++ program
Rémy Sigrist, PARI program
EXAMPLE
The first terms, alongside an appropriate set of points, are:
n a(n) Points
-- ---- -----------------------------------
1 1 N/A
2 1 (1,1)
3 2 (1,1), (2,1)
4 2 (1,1), (3,2)
5 2 (1,1), (4,2)
6 3 (3,2), (4,2), (5,2)
7 3 (2,1), (4,2), (6,3)
8 3 (1,1), (4,2), (7,3)
9 3 (2,1), (5,2), (8,3)
10 4 (6,3), (7,3), (8,3), (9,3)
11 4 (1,1), (4,2), (7,3), (10,4)
12 4 (2,1), (5,2), (8,3), (11,4)
13 3 (4,2), (8,3), (12,4)
14 5 (6,3), (7,3), (8,3), (9,3), (13,3)
15 5 (2,1), (5,2), (8,3), (11,4), (14,5)
PROG
(C++) // See Links section.
(PARI) \\ See Links section.
CROSSREFS
Sequence in context: A331255 A362881 A317359 * A108229 A023966 A368942
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Aug 14 2024
STATUS
approved