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A341829 Irregular triangle read by rows: the n-th row gives the x-values of the solutions of the equation x*(y - 1) + (2*x - y - 1)*(x mod 2) = 2*n for 0 < x <= y.

%I A341829 #14 Oct 23 2022 09:20:12
%S A341829 2,2,2,2,3,2,3,2,3,4,2,3,2,3,4,2,3,2,3,4,2,3,2,3,4,5,2,3,2,3,4,5,2,3,
%T A341829 6,2,3,4,5,2,3,2,3,4,5,6,2,3,2,3,4,5,2,3,6,2,3,4,5,2,3,2,3,4,5,6,7,2,
%U A341829 3,2,3,4,5,2,3,6,7,2,3,4,5,8,2,3,2,3,4,5,6,7
%N A341829 Irregular triangle read by rows: the n-th row gives the x-values of the solutions of the equation x*(y - 1) + (2*x - y - 1)*(x mod 2) = 2*n for 0 < x <= y.
%C A341829 Equivalently, the n-th row gives the column indices corresponding to 2*n + 1 in the triangle A340804.
%H A341829 Stefano Spezia, <a href="/A341829/b341829.txt">Table of n, a(n) for n = 1..10175</a> (first 1500 rows of the triangle, flattened).
%e A341829 Triangle begins:
%e A341829 2
%e A341829 2
%e A341829 2
%e A341829 2   3
%e A341829 2   3
%e A341829 2   3   4
%e A341829 2   3
%e A341829 2   3   4
%e A341829 2   3
%e A341829 2   3   4
%e A341829 2   3
%e A341829 2   3   4   5
%e A341829 2   3
%e A341829 2   3   4   5
%e A341829 2   3   6
%e A341829 2   3   4   5
%e A341829 2   3
%e A341829 2   3   4   5   6
%e A341829 ...
%t A341829 Table[Union[2Intersection[Divisors[n],Table[d,{d,Floor[(1+Sqrt[1+8n])/4]}]],2Intersection[Divisors[n],Table[d,{d,Floor[(Sqrt[1+2n]-1)/2]}]]+1],{n,30}]//Flatten
%Y A341829 Cf. A005843, A340804, A340805 (row length or solutions number), A341830 (y-values).
%K A341829 nonn,tabf
%O A341829 1,1
%A A341829 _Stefano Spezia_, Feb 21 2021