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.
4, 7, 9, 13, 16, 18, 25, 27, 34, 43, 49, 57, 60, 64, 70, 73, 81, 87, 93, 99, 100, 102, 111, 112, 114, 121, 123, 127, 133, 144, 148, 150, 157, 160, 165, 169, 175, 183, 186, 189, 196, 202, 207, 211, 214, 219, 225, 235, 241, 244, 249, 255, 256, 258, 262, 265, 273
Offset: 1
Keywords
Examples
Hypotenuses A376210
4k+1 | A376211
k A008846 | | A376208
| | Sorted legs [x,y] of | | | A375750
| | Pythagorean triangles | | | | A376209
1 5 [3,4] . X . X .
3 13 [5,12] . X . X .
4 17 [8,15] X . X . .
6 25 [7,24] . X . X .
7 29 [20,21] X . X . .
9 37 [12,35] X . X . .
10 41 [9,40] . X . X .
13 53 [28,45] X . X . .
15 61 [11,60] . X . X .
16 65 [16,63],[33,56],[39,52] X . X X X
18 73 [48,55] X . X . .
21 85 [13,84],[36,77],[51,68] . X X X X
Programs
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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)
Comments