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).
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
Keywords
Examples
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)
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..10000
- Rémy Sigrist, C++ program
- Rémy Sigrist, PARI program
Programs
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PARI
\\ See Links section.
Comments