A264482 - OEIS

%I #44 Jun 25 2016 01:47:59

%S 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,

%T 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,

%U 9,11,13,17,19,23,25,29,31,1,2,3,5,7,11,13,17,19

%N 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.

%C 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.

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

%C Are there infinitely many rows that start with 1?

%H Max Barrentine, <a href="/A264482/b264482.txt">Table of n, a(n) for n = 1..1081, rows 1..46.</a>

%e 1;

%e 1, 2;

%e 1, 2, 3;

%e 1, 2, 3, 5;

%e 1, 2, 3, 5, 7;

%e 5, 7, 8, 9, 11, 13;

%e ...

%Y Cf. A260652.

%K nonn,tabl

%O 1,3

%A _Max Barrentine_, Nov 14 2015

%E b-file corrected and extended by _Max Barrentine_, Jun 23 2016