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 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). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 2 23:17 EST 2023. Contains 367526 sequences. (Running on oeis4.)