A375030 Irregular triangle T(n, k), n > 0, k = 1..A373797(n), read by rows; the n-th row corresponds to the lexicographically earliest sequence S of A373797(n) distinct integers in the range 1..n such that for any prime number p, any run of consecutive multiples of p in S has length exactly 2.

1, 1, 1, 1, 2, 4, 1, 2, 4, 1, 2, 6, 3, 1, 2, 6, 3, 1, 2, 4, 3, 6, 8, 1, 2, 4, 3, 6, 8, 1, 2, 4, 3, 9, 5, 10, 8, 1, 2, 4, 3, 9, 5, 10, 8, 1, 2, 4, 3, 6, 8, 5, 10, 12, 9, 1, 2, 4, 3, 6, 8, 5, 10, 12, 9, 1, 2, 4, 3, 6, 10, 5, 7, 14, 12, 9, 1, 2, 4, 3, 6, 8, 5, 15, 12, 14, 7

Offset: 1

Author

Rémy Sigrist at the suggestion of Peter Luschny, Jul 28 2024

Keywords

• nonn
• tabf

Examples

			Triangle T(n, k) begins:
    1;
    1;
    1;
    1, 2, 4;
    1, 2, 4;
    1, 2, 6, 3;
    1, 2, 6, 3;
    1, 2, 4, 3, 6, 8;
    1, 2, 4, 3, 6, 8;
    1, 2, 4, 3, 9, 5, 10, 8;
    1, 2, 4, 3, 9, 5, 10, 8;
    1, 2, 4, 3, 6, 8, 5, 10, 12, 9;
    1, 2, 4, 3, 6, 8, 5, 10, 12, 9;
    1, 2, 4, 3, 6, 10, 5, 7, 14, 12, 9;
    1, 2, 4, 3, 6, 8, 5, 15, 12, 14, 7;
    1, 2, 4, 3, 6, 8, 5, 10, 12, 9, 7, 14, 16;
    1, 2, 4, 3, 6, 8, 5, 10, 12, 9, 7, 14, 16;
    1, 2, 4, 3, 6, 8, 5, 15, 9, 16, 14, 7, 12, 18;
    1, 2, 4, 3, 6, 8, 5, 15, 9, 16, 14, 7, 12, 18;
    ...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..386 (rows for n = 1..31 flattened)
• Rémy Sigrist, PARI program.
• Peter Luschny, Maple program.

Crossrefs

Cf. A280864, A373797.

Programs

Maple

# See Links section.

PARI

\\ See Links section.