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

1,1

Links

Table of n, a(n) for n=1..57.

Example

       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

Prog

(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)

Crossrefs

({A087937}-1)/4 is a subsequence.

A094178 \ A376211.

Cf. A375750, A376208.

Sequence in context: A310959 A310960 A376208 * A108287 A230240 A243175

Adjacent sequences: A376207 A376208 A376209 * A376211 A376212 A376213

Keyword

nonn

Author

Hugo Pfoertner, Sep 21 2024

Status

approved