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A375422
a(n) is the maximum number of points from the set {(k, prime(k)), k = 1..n} belonging to a straight line passing through the point (n, prime(n)) (where prime(k) denotes the k-th prime number).
5
1, 2, 2, 3, 2, 2, 3, 3, 4, 3, 3, 4, 5, 4, 5, 6, 3, 7, 4, 5, 8, 6, 7, 3, 3, 3, 4, 4, 3, 4, 4, 4, 5, 3, 4, 5, 6, 5, 7, 4, 4, 6, 5, 5, 8, 4, 5, 6, 6, 4, 4, 4, 5, 4, 5, 6, 7, 5, 4, 5, 4, 5, 5, 8, 5, 4, 6, 7, 7, 8, 9, 10, 9, 10, 11, 11, 12, 12, 13, 13, 8, 14, 9, 15
OFFSET
1,2
COMMENTS
Is this sequence unbounded?
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 (1,2)
2 2 (1,2), (2,3)
3 2 (1,2), (3,5)
4 3 (2,3), (3,5), (4,7)
5 2 (1,2), (5,11)
6 2 (1,2), (6,13)
7 3 (3,5), (5,11), (7,17)
8 3 (2,3), (5,11), (8,19)
9 4 (3,5), (5,11), (7,17), (9,23)
10 3 (6,13), (7,17), (10,29)
11 3 (8,19), (9,23), (11,31)
12 4 (6,13), (7,17), (10,29), (12,37)
13 5 (6,13), (7,17), (10,29), (12,37), (13,41)
14 4 (8,19), (9,23), (11,31), (14,43)
15 5 (8,19), (9,23), (11,31), (14,43), (15,47)
16 6 (6,13), (7,17), (10,29), (12,37), (13,41), (16,53)
PROG
(C++) // See Links section.
(PARI) \\ See Links section.
CROSSREFS
Sequence in context: A187182 A362816 A176208 * A330623 A153095 A254574
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Aug 14 2024
STATUS
approved