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A376571 Table T(n, k), n > 1, k = 1..n-1, read by rows; T(n, k) is the greatest 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 A376571 #6 Sep 30 2024 10:57:31
%S A376571 2,3,4,4,4,4,5,8,9,23,6,6,6,8,6,7,7,9,7,9,21,8,8,8,8,8,8,8,9,9,9,9,9,
%T A376571 9,9,15,10,10,10,10,15,21,21,52,152,11,11,11,11,11,11,11,15,15,11,12,
%U A376571 12,12,12,12,21,21,12,12,21,153,13,13,13,13,13,21,21,28,17,21,53,21
%N A376571 Table T(n, k), n > 1, k = 1..n-1, read by rows; T(n, k) is the greatest 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 A376571 Rémy Sigrist, <a href="/A376571/b376571.txt">Table of n, a(n) for n = 2..10012</a> (rows for n = 2..142 flattened)
%F A376571 T(n, k) >= n.
%e A376571 Table T(n, k) begins:
%e A376571     2;
%e A376571     3, 4;
%e A376571     4, 4, 4;
%e A376571     5, 8, 9, 23;
%e A376571     6, 6, 6, 8, 6;
%e A376571     7, 7, 9, 7, 9, 21;
%e A376571     8, 8, 8, 8, 8, 8, 8;
%e A376571     9, 9, 9, 9, 9, 9, 9, 15;
%e A376571     10, 10, 10, 10, 15, 21, 21, 52, 152;
%e A376571     11, 11, 11, 11, 11, 11, 11, 15, 15, 11;
%e A376571     12, 12, 12, 12, 12, 21, 21, 12, 12, 21, 153;
%e A376571     13, 13, 13, 13, 13, 21, 21, 28, 17, 21, 53, 21;
%e A376571     ...
%o A376571 (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 = -oo); forprime (y2 = 2, 1+maxp, x2++; if (x0 * (y1 - y2) + x1 * (y2 - y0) + x2 * (y0 - y1)==0, v = x2;);); return (v); }
%Y A376571 Cf. A376187, A376569, A376570.
%K A376571 nonn,tabl
%O A376571 2,1
%A A376571 _Rémy Sigrist_, Sep 28 2024