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%I #12 Apr 19 2020 05:21:58
%S 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,
%T 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,
%U 10,5,5,7,6,10,10,10,11,11,12,15,12,13,13,11
%N 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).
%C 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.
%H Rémy Sigrist, <a href="/A334046/b334046.txt">Table of n, a(n) for n = 1..10000</a>
%e For n = 4:
%e - we consider the following points:
%e . . . X
%e / (4,7)
%e . . . / .
%e /
%e . . X .
%e / (3,5)
%e . . / . .
%e /
%e . X . .
%e (2,3)
%e X . . .
%e (1,2)
%e . . . .
%e - (2,3) is not visible from (4,7) (as it is hidden by (3,5)),
%e - whereas (1,2) and (3,5) are visible from (4,7),
%e - hence a(4) = 1.
%o (PARI) g(z) = z/gcd(real(z), imag(z))
%o for (n=1, 81, print1 (n-1-#Set(apply(k -> g((k+prime(k)*I)-(n+prime(n)*I)), [1..n-1]))", "))
%Y Cf. A000040, A334043.
%K nonn
%O 1,8
%A _Rémy Sigrist_, Apr 13 2020
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