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

1,2

Comments

Is this sequence unbounded?

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

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

Cf. A334046, A375386.

Sequence in context: A187182 A362816 A176208 * A330623 A153095 A254574

Adjacent sequences: A375419 A375420 A375421 * A375423 A375424 A375425

Keyword

nonn

Author

Rémy Sigrist, Aug 14 2024

Status

approved