A375420 a(n) is the number of straight lines passing through the points (i, prime(i)) and (j, prime(j)) with i < j <= n (where prime(k) denotes the k-th prime number).

0, 1, 3, 4, 8, 13, 17, 20, 25, 32, 40, 48, 56, 66, 74, 84, 94, 105, 120, 135, 148, 162, 176, 191, 211, 230, 247, 267, 287, 306, 333, 361, 385, 410, 437, 462, 488, 517, 545, 571, 601, 633, 663, 696, 730, 761, 796, 836, 879, 921, 962, 1000, 1038, 1080, 1122

Offset

1,3

Links

Table of n, a(n) for n=1..55.

Formula

a(n) <= A000217(n+1).

Example

The first terms, alongside the new lines passing through (n, prime(n)), are:
  n  a(n)  New lines passing through (n, prime(n))
  -  ----  --------------------------------------------
  1     0  {}
  2     1  {x + 1}
  3     3  {2*x - 1, 3/2*x + 1/2}
  4     4  {5/3*x + 1/3}
  5     8  {4*x - 9, 3*x - 4, 8/3*x - 7/3, 9/4*x - 1/4}

Prog

(PARI) { L = []; for (n = 1, #p = primes(55), print1 (#L = setunion(L, Set(vector(n-1, i, polinterpolate([i, n], [p[i], p[n]]))))", "); ); }

Crossrefs

Cf. A000217, A375421.

Sequence in context: A153339 A275989 A343562 * A033955 A327466 A049720

Adjacent sequences: A375417 A375418 A375419 * A375421 A375422 A375423

Keyword

nonn,changed

Author

Rémy Sigrist, Aug 14 2024

Status

approved