login
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).
3
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, 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, 2, 2, 2, 8, 8, 3, 3, 8, 5, 8, 2, 2, 2, 2, 2, 2, 2, 5, 5, 2, 5, 2, 2
OFFSET
2,1
LINKS
Rémy Sigrist, Table of n, a(n) for n = 2..10012 (rows for n = 2..142 flattened)
FORMULA
T(n, k) >= 2.
EXAMPLE
Table T(n, k) begins:
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, 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, 2, 2, 2, 8, 8, 3, 3, 8, 5, 8;
...
PROG
(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); }
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Rémy Sigrist, Sep 28 2024
STATUS
approved