A326309 Ordered perimeters p of primitive Pythagorean triangles having short leg in common with the long leg or hypotenuse of a primitive Pythagorean triangle with perimeter < p, and also having both the long leg and the hypotenuse in common with the short legs of primitive Pythagorean triangles with perimeter > p.

30, 84, 182, 234, 240, 260, 306, 312, 374, 462, 476, 510, 532, 546, 570, 650, 828, 840, 870, 900, 920, 966, 986, 1050, 1100, 1188, 1254, 1260, 1276, 1320, 1330, 1364, 1392, 1406, 1508, 1554, 1612, 1624, 1716, 1722, 1736, 1794, 1820, 1850, 1860, 1886, 2070, 2214, 2220

Offset

1,1

Comments

The short leg of a primitive Pythagorean triangle of perimeter a(n) is either the long leg or hypotenuse of a triangle whose perimeter is less than a(n).

The long leg and the hypotenuse of a triangle with perimeter a(n) are the short legs of triangles with perimeter greater than a(n).

This sequence is a subsequence of A024364. A subsequence of this sequence exists after applying the restrictions imposed by the sequence title to the sequence itself and begins a(2), a(3), a(9), a(11), ... . Applying the same restrictions on {a(2), a(3), a(9), a(11), ...} gives a sequence a(9), a(11), a(22), a(25), ... .

Question: Does recursive application of this sequence to A024364 terminate?

Links

Table of n, a(n) for n=1..49.

Example

30 is a term because 30 = 5+12+13 and 12 = 3+4+5 and 84 = 12+35+37 and 182 = 13+84+85.
84 is a term because 84 = 12+35+37 and 30 = 5+12+13 and 1260 = 35+612+613 and 1406 = 37+684+685.
182 is a term because 182 = 13+84+85 and 30 = 5+12+13 and 476 = 84+187+205 and 374 = 85+132+157.

Crossrefs

Subsequence of A024364.

Sequence in context: A165772 A277980 A241025 * A326838 A098996 A130862

Adjacent sequences: A326306 A326307 A326308 * A326310 A326311 A326312

Keyword

nonn

Author

Torlach Rush, Oct 17 2019

Status

approved