This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A376210 #6 Sep 22 2024 15:20:54
%S A376210 4,7,9,13,16,18,25,27,34,43,49,57,60,64,70,73,81,87,93,99,100,102,111,
%T A376210 112,114,121,123,127,133,144,148,150,157,160,165,169,175,183,186,189,
%U A376210 196,202,207,211,214,219,225,235,241,244,249,255,256,258,262,265,273
%N A376210 Numbers k for which among all possible Pythagorean triangles with the hypotenuse 4*k+1, the minimum of the lengths of the shorter legs is even.
%e A376210 Hypotenuses A376210
%e A376210 4k+1 | A376211
%e A376210 k A008846 | | A376208
%e A376210 | | Sorted legs [x,y] of | | | A375750
%e A376210 | | Pythagorean triangles | | | | A376209
%e A376210 1 5 [3,4] . X . X .
%e A376210 3 13 [5,12] . X . X .
%e A376210 4 17 [8,15] X . X . .
%e A376210 6 25 [7,24] . X . X .
%e A376210 7 29 [20,21] X . X . .
%e A376210 9 37 [12,35] X . X . .
%e A376210 10 41 [9,40] . X . X .
%e A376210 13 53 [28,45] X . X . .
%e A376210 15 61 [11,60] . X . X .
%e A376210 16 65 [16,63],[33,56],[39,52] X . X X X
%e A376210 18 73 [48,55] X . X . .
%e A376210 21 85 [13,84],[36,77],[51,68] . X X X X
%o A376210 (PARI) is_a376210_1(n,r=0) = my(c=4*n+1, q=qfbsolve(Qfb(1,0,1), c^2, 3), qd=#q); if(qd<2, 0, my(a=vecmin(abs(concat(q))[1..2*(qd-1)]), b=sqrtint(c^2-a^2)); a%2==r && gcd([a,b,c])==1)
%Y A376210 ({A087937}-1)/4 is a subsequence.
%Y A376210 A094178 \ A376211.
%Y A376210 Cf. A375750, A376208.
%K A376210 nonn
%O A376210 1,1
%A A376210 _Hugo Pfoertner_, Sep 21 2024