A286511 - OEIS

A286511

Lexicographically earliest sequence of positive integers such that for each pair (i, j) with i < j, the 2 X 2 matrix [i, a(i); j, a(j)] has a distinct determinant.

%I #9 May 11 2017 13:43:59

%S 1,1,3,1,7,10,17,1,22,29,35,40,28,74,5,1,70,73,90,109,103,125,30,89,

%T 158,172,165,123,171,212,228,262,242,52,264,274,167,349,1,383,288,423,

%U 404,445,412,394,514,427,478,527,626,229,602,581,536,665,710,698

%N Lexicographically earliest sequence of positive integers such that for each pair (i, j) with i < j, the 2 X 2 matrix [i, a(i); j, a(j)] has a distinct determinant.

%H Peter Kagey, <a href="/A286511/b286511.txt">Table of n, a(n) for n = 1..1000</a>

%e For n = 3:

%e a(3) != 1 or else det([1, 1; 2, 1]) = -1 = det([1, 1; 3, 1]);

%e a(3) != 2 or else det([1, 1; 2, 1]) = -1 = det([1, 1; 3, 2]); therefore,

%e a(3) = 3.

%K nonn

%O 1,3

%A _Peter Kagey_, May 10 2017