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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).
3
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, 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, 2, 3, 4, 5, 6, 6, 8, 9, 6, 11, 6, 1, 2, 3, 4, 5, 6, 7, 8, 8, 10, 8, 12, 13
OFFSET
2,3
LINKS
Rémy Sigrist, Table of n, a(n) for n = 2..10012 (rows for n = 2..142 flattened)
FORMULA
T(n, k) <= k.
T(n, 1) = 1.
EXAMPLE
Triangle T(n, k) begins:
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, 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, 2, 3, 4, 5, 6, 6, 8, 9, 6, 11, 6;
...
PROG
(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); ); ); }
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Rémy Sigrist, Sep 28 2024
STATUS
approved