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).
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, 9, 9, 15, 10, 10, 10, 10, 15, 21, 21, 52, 152, 11, 11, 11, 11, 11, 11, 11, 15, 15, 11, 12, 12, 12, 12, 12, 21, 21, 12, 12, 21, 153, 13, 13, 13, 13, 13, 21, 21, 28, 17, 21, 53, 21
Offset: 2
Examples
Table T(n, k) begins:
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, 9, 9, 15;
10, 10, 10, 10, 15, 21, 21, 52, 152;
11, 11, 11, 11, 11, 11, 11, 15, 15, 11;
12, 12, 12, 12, 12, 21, 21, 12, 12, 21, 153;
13, 13, 13, 13, 13, 21, 21, 28, 17, 21, 53, 21;
...
Links
- Rémy Sigrist, Table of n, a(n) for n = 2..10012 (rows for n = 2..142 flattened)
Programs
-
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); }
Formula
T(n, k) >= n.