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A376570 Table T(n, k), n > 1, k = 1..n-1, read by rows; T(n, k) is the least m such that the points (m, prime(m)), (k, prime(k)) and (n, prime(n)) are aligned (where prime(k) denotes the k-th prime number).

%I A376570 #7 Sep 30 2024 10:57:36
%S A376570 1,1,2,1,2,2,1,2,3,4,1,2,3,4,5,1,2,3,4,3,6,1,2,3,4,2,4,7,1,2,3,4,3,6,
%T A376570 3,8,1,2,3,4,5,6,6,8,9,1,2,3,4,5,6,7,8,8,10,1,2,3,4,5,6,6,8,9,6,11,1,
%U A376570 2,3,4,5,6,6,8,9,6,11,6,1,2,3,4,5,6,7,8,8,10,8,12,13
%N A376570 Table T(n, k), n > 1, k = 1..n-1, read by rows; T(n, k) is the least m such that the points (m, prime(m)), (k, prime(k)) and (n, prime(n)) are aligned (where prime(k) denotes the k-th prime number).
%H A376570 Rémy Sigrist, <a href="/A376570/b376570.txt">Table of n, a(n) for n = 2..10012</a> (rows for n = 2..142 flattened)
%H A376570 Rémy Sigrist, <a href="/A376570/a376570.png">Scatterplot of (n, k) such that T(n, k) = k and n <= 1000</a>
%F A376570 T(n, k) <= k.
%F A376570 T(n, 1) = 1.
%e A376570 Triangle T(n, k) begins:
%e A376570     1;
%e A376570     1, 2;
%e A376570     1, 2, 2;
%e A376570     1, 2, 3, 4;
%e A376570     1, 2, 3, 4, 5;
%e A376570     1, 2, 3, 4, 3, 6;
%e A376570     1, 2, 3, 4, 2, 4, 7;
%e A376570     1, 2, 3, 4, 3, 6, 3, 8;
%e A376570     1, 2, 3, 4, 5, 6, 6, 8, 9;
%e A376570     1, 2, 3, 4, 5, 6, 7, 8, 8, 10;
%e A376570     1, 2, 3, 4, 5, 6, 6, 8, 9, 6, 11;
%e A376570     1, 2, 3, 4, 5, 6, 6, 8, 9, 6, 11, 6;
%e A376570     ...
%o A376570 (PARI) T(n,k) = { my (x0 = k, y0 = prime(x0), x1 = n, y1 = prime(x1), x2 = 0); forprime (y2 = 2, oo, x2++; if (x0 * (y1 - y2) + x1 * (y2 - y0) + x2 * (y0 - y1)==0, return (x2););); }
%Y A376570 Cf. A376187, A376569, A376571.
%K A376570 nonn,tabl
%O A376570 2,3
%A A376570 _Rémy Sigrist_, Sep 28 2024