A264482 Triangle T(n,k) (1 <= k <= n) read by rows: row n lists the set of n coprime numbers that minimizes the difference between first and last terms, and then minimizes the average of the terms.

1, 1, 2, 1, 2, 3, 1, 2, 3, 5, 1, 2, 3, 5, 7, 5, 7, 8, 9, 11, 13, 1, 2, 3, 5, 7, 11, 13, 5, 7, 8, 9, 11, 13, 17, 19, 1, 2, 3, 5, 7, 11, 13, 17, 19, 11, 13, 16, 17, 19, 21, 23, 25, 29, 31, 7, 8, 9, 11, 13, 17, 19, 23, 25, 29, 31, 1, 2, 3, 5, 7, 11, 13, 17, 19

Offset: 1

Author

Max Barrentine, Nov 14 2015

Keywords

• nonn
• tabl

Comments

The minimal set of the (k+n)th row is determined by the minimal k-tuple coprime to the n-th primorial, where every prime <= the n-th prime must be a factor of some number in the set. E.g., the sixth row must consist of numbers congruent to 5, 7, 11 and 13 mod 6, as well as one term with a factor of 2 and another with a factor of 3.

In cases where multiple k-tuples satisfy the definition, the lexicographically earliest solution is chosen.

Are there infinitely many rows that start with 1?

Examples

			1;
1, 2;
1, 2, 3;
1, 2, 3, 5;
1, 2, 3, 5, 7;
5, 7, 8, 9, 11, 13;
...
		

Links

• Max Barrentine, Table of n, a(n) for n = 1..1081, rows 1..46.

Crossrefs

Cf. A260652.

Extensions

b-file corrected and extended by Max Barrentine, Jun 23 2016