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

1,2

Comments

Is this sequence unbounded?

Links

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

Rémy Sigrist, PARI program

Example

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)

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A375422.

Sequence in context: A321576 A304101 A278636 * A126336 A364421 A352631

Adjacent sequences: A376494 A376495 A376496 * A376498 A376499 A376500

Keyword

nonn

Author

Rémy Sigrist, Sep 25 2024

Status

approved