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A376569 Table T(n, k), n > 1, k = 1..n-1, read by rows; T(n, k) is the number of points of the form (m, prime(m)) aligned with the points (k, prime(k)) and (n, prime(n)) (where prime(k) denotes the k-th prime number).

%I A376569 #7 Sep 30 2024 10:57:43
%S A376569 2,2,3,2,3,3,2,3,4,7,2,2,2,3,2,2,2,4,2,4,8,2,3,2,3,3,3,2,2,2,4,2,4,2,
%T A376569 4,5,2,2,2,2,3,8,8,4,6,2,2,2,2,2,2,2,5,5,2,2,2,2,2,2,8,8,2,2,8,6,2,2,
%U A376569 2,2,2,8,8,3,3,8,5,8,2,2,2,2,2,2,2,5,5,2,5,2,2
%N A376569 Table T(n, k), n > 1, k = 1..n-1, read by rows; T(n, k) is the number of points of the form (m, prime(m)) aligned with the points (k, prime(k)) and (n, prime(n)) (where prime(k) denotes the k-th prime number).
%H A376569 Rémy Sigrist, <a href="/A376569/b376569.txt">Table of n, a(n) for n = 2..10012</a> (rows for n = 2..142 flattened)
%F A376569 T(n, k) >= 2.
%e A376569 Table T(n, k) begins:
%e A376569     2;
%e A376569     2, 3;
%e A376569     2, 3, 3;
%e A376569     2, 3, 4, 7;
%e A376569     2, 2, 2, 3, 2;
%e A376569     2, 2, 4, 2, 4, 8;
%e A376569     2, 3, 2, 3, 3, 3, 2;
%e A376569     2, 2, 4, 2, 4, 2, 4, 5;
%e A376569     2, 2, 2, 2, 3, 8, 8, 4, 6;
%e A376569     2, 2, 2, 2, 2, 2, 2, 5, 5, 2;
%e A376569     2, 2, 2, 2, 2, 8, 8, 2, 2, 8, 6;
%e A376569     2, 2, 2, 2, 2, 8, 8, 3, 3, 8, 5, 8;
%e A376569     ...
%o A376569 (PARI) T(n,k) = { my (x0 = k, y0 = prime(x0), x1 = n, y1 = prime(x1), s = (y1-y0)/(x1-x0), maxp = max(60184, exp(max(y0/x0, s) + 1.1)), x2 = 0, v = 0); forprime (y2 = 2, 1+maxp, x2++; if (x0 * (y1 - y2) + x1 * (y2 - y0) + x2 * (y0 - y1)==0, v++;);); return (v); }
%Y A376569 Cf. A376187, A376570, A376571.
%K A376569 nonn,tabl
%O A376569 2,1
%A A376569 _Rémy Sigrist_, Sep 28 2024