A375421 a(n) is the number of distinct straight lines passing through the points (k, prime(k)) and (n, prime(n)) for k < n (where prime(k) denotes the k-th prime number).

0, 1, 2, 2, 4, 5, 5, 5, 6, 8, 9, 9, 9, 11, 10, 11, 13, 12, 16, 16, 14, 16, 16, 19, 22, 22, 21, 23, 24, 23, 28, 29, 27, 29, 30, 29, 29, 32, 31, 32, 34, 35, 35, 37, 36, 37, 39, 42, 44, 45, 45, 43, 44, 47, 47, 48, 48, 49, 46, 49, 49, 49, 56, 56, 53, 55, 61, 62

Offset

1,3

Links

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

Formula

a(n) <= n-1.

Example

The first terms, alongside the corresponding lines, are:  n  a(n)  Lines
  -  ----  --------------------------------------------------------------
  1     0  {}
  2     1  {x + 1}
  3     2  {2*x - 1, 3/2*x + 1/2}
  4     2  {2*x - 1, 5/3*x + 1/3}
  5     4  {4*x - 9, 3*x - 4, 8/3*x - 7/3, 9/4*x - 1/4}
  6     5  {3*x - 5, 8/3*x - 3, 5/2*x - 2, 2*x + 1, 11/5*x - 1/5}
  7     5  {4*x - 11, 3*x - 4, 10/3*x - 19/3, 14/5*x - 13/5, 5/2*x - 1/2}

Prog

(PARI) { for (n = 1, #p = primes(68), print1 (#Set(vector(n-1, i, polinterpolate([i, n], [p[i], p[n]])))", "); ); }

Crossrefs

Cf. A375420.

Sequence in context: A361645 A319409 A122543 * A334149 A369452 A118003

Adjacent sequences: A375418 A375419 A375420 * A375422 A375423 A375424

Keyword

nonn

Author

Rémy Sigrist, Aug 14 2024

Status

approved