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%I #42 Nov 07 2019 13:42:47
%S 30,84,182,234,240,260,306,312,374,462,476,510,532,546,570,650,828,
%T 840,870,900,920,966,986,1050,1100,1188,1254,1260,1276,1320,1330,1364,
%U 1392,1406,1508,1554,1612,1624,1716,1722,1736,1794,1820,1850,1860,1886,2070,2214,2220
%N 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.
%C 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).
%C 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).
%C 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), ... .
%C Question: Does recursive application of this sequence to A024364 terminate?
%e 30 is a term because 30 = 5+12+13 and 12 = 3+4+5 and 84 = 12+35+37 and 182 = 13+84+85.
%e 84 is a term because 84 = 12+35+37 and 30 = 5+12+13 and 1260 = 35+612+613 and 1406 = 37+684+685.
%e 182 is a term because 182 = 13+84+85 and 30 = 5+12+13 and 476 = 84+187+205 and 374 = 85+132+157.
%Y Subsequence of A024364.
%K nonn
%O 1,1
%A _Torlach Rush_, Oct 17 2019