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).

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)

Rémy Sigrist, Scatterplot of (n, k) such that T(n, k) = k and n <= 1000

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

Cf. A376187, A376569, A376571.

Sequence in context: A132749 A271106 A273673 * A140186 A078498 A350700

Adjacent sequences: A376567 A376568 A376569 * A376571 A376572 A376573

Keyword

nonn,tabl

Author

Rémy Sigrist, Sep 28 2024

Status

approved