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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.
5
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
1,3
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?
EXAMPLE
1;
1, 2;
1, 2, 3;
1, 2, 3, 5;
1, 2, 3, 5, 7;
5, 7, 8, 9, 11, 13;
...
CROSSREFS
Cf. A260652.
Sequence in context: A119444 A060040 A092080 * A193588 A165884 A263939
KEYWORD
nonn,tabl
AUTHOR
Max Barrentine, Nov 14 2015
EXTENSIONS
b-file corrected and extended by Max Barrentine, Jun 23 2016
STATUS
approved