A334046 a(n) is the number of points of the set { (k, prime(k)), k = 1..n-1 } that are not visible from the point (n, prime(n)) (where prime(n) denotes the n-th prime number).

0, 0, 0, 1, 0, 0, 1, 2, 2, 1, 1, 2, 3, 2, 4, 4, 3, 5, 2, 3, 6, 5, 6, 4, 2, 3, 5, 4, 4, 6, 2, 2, 5, 4, 4, 6, 7, 5, 7, 7, 6, 6, 7, 6, 8, 8, 7, 5, 4, 4, 5, 8, 8, 6, 7, 7, 8, 8, 12, 10, 11, 12, 6, 7, 11, 10, 5, 5, 7, 6, 10, 10, 10, 11, 11, 12, 15, 12, 13, 13, 11

Offset

1,8

Comments

For any i and k such that i < k: the point (i, prime(i)) is visible from the point (k, prime(k)) if there are no j such that i < j < k and the three points (i, prime(i)), (j, prime(j)), (k, prime(k)) are aligned.

Links

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

Example

For n = 4:
- we consider the following points:
     .   .   .   X
                / (4,7)
     .   .   . / .
              /
     .   .   X   .
            / (3,5)
     .   . / .   .
          /
     .   X   .   .
          (2,3)
     X   .   .   .
      (1,2)
     .   .   .   .
- (2,3) is not visible from (4,7) (as it is hidden by (3,5)),
- whereas (1,2) and (3,5) are visible from (4,7),
- hence a(4) = 1.

Prog

(PARI) g(z) = z/gcd(real(z), imag(z))
for (n=1, 81, print1 (n-1-#Set(apply(k -> g((k+prime(k)*I)-(n+prime(n)*I)), [1..n-1]))", "))

Crossrefs

Cf. A000040, A334043.

Sequence in context: A305825 A366780 A324029 * A136605 A165621 A284321

Adjacent sequences: A334043 A334044 A334045 * A334047 A334048 A334049

Keyword

nonn

Author

Rémy Sigrist, Apr 13 2020

Status

approved