

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
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OFFSET

1,3


COMMENTS

The minimal set of the (k+n)th row is determined by the minimal ktuple coprime to the nth primorial, where every prime <= the nth 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 ktuples satisfy the definition, the lexicographically earliest solution is chosen.
Are there infinitely many rows that start with 1?


LINKS

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


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
Adjacent sequences: A264479 A264480 A264481 * A264483 A264484 A264485


KEYWORD

nonn,tabl


AUTHOR

Max Barrentine, Nov 14 2015


EXTENSIONS

bfile corrected and extended by Max Barrentine, Jun 23 2016


STATUS

approved



