A376497 a(n) is the maximum number of points from the set {(prime(k), prime(k+1)), k = 1..n} belonging to a straight line passing through the point (prime(n), prime(n+1)) (where prime(k) denotes the k-th prime number).

1, 2, 2, 2, 3, 2, 4, 3, 3, 5, 2, 4, 6, 5, 3, 4, 7, 5, 6, 8, 6, 7, 7, 3, 8, 9, 9, 10, 10, 3, 11, 8, 11, 3, 12, 9, 10, 12, 11, 12, 13, 3, 14, 13, 15, 3, 2, 14, 16, 15, 13, 17, 3, 14, 15, 16, 18, 17, 16, 19, 4, 4, 17, 20, 18, 3, 18, 5, 21, 19, 19, 3, 20, 21, 20

Offset: 1

Author

Rémy Sigrist, Sep 25 2024

Keywords

• nonn

Comments

Is this sequence unbounded?

Examples

			The first terms, alongside an appropriate set of points, are:
  n   a(n)  Points
  --  ----  ------------------------------------------------
   1     1  (2,3)
   2     2  (2,3), (3,5)
   3     2  (3,5), (5,7)
   4     2  (5,7), (7,11)
   5     3  (3,5), (5,7), (11,13)
   6     2  (7,11), (13,17)
   7     4  (3,5), (5,7), (11,13), (17,19)
   8     3  (7,11), (13,17), (19,23)
   9     3  (3,5), (13,17), (23,29)
  10     5  (3,5), (5,7), (11,13), (17,19), (29,31)
  11     2  (23,29), (31,37)
  12     4  (7,11), (13,17), (19,23), (37,41)
  13     6  (3,5), (5,7), (11,13), (17,19), (29,31), (41,43)
  14     5  (7,11), (13,17), (19,23), (37,41), (43,47)
  15     3  (23,29), (31,37), (47,53)
  16     4  (23,29), (31,37), (47,53), (53,59)
		

Links

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

Crossrefs

Cf. A375422.

Programs

PARI

\\ See Links section.