A088319 Ordered hypotenuses of primitive Pythagorean triangles having legs that add up to a square.

41, 205, 389, 689, 1565, 1625, 1781, 3865, 4105, 4549, 5989, 7421, 9161, 9685, 10225, 10685, 13025, 17509, 17965, 18329, 21349, 21701, 25801, 33161, 33169, 33529, 36749, 38581, 39709, 49325, 51649, 52429, 52721, 56785, 57065, 67205, 70801

Offset: 1

Author

Lekraj Beedassy, Nov 06 2003

Keywords

• nonn

Examples

			9161 is in the sequence because of the triple 5289^2 + 7480^2 = 9161^2 where we have 5289+7480=113^2.
Similarly, 205 belongs to the triple (133,156,205) and 133+156=17^2.
		

References

• F. Rubin, "Squared" Pythagorean Triples, Solution to problem 2306, J. Recreational Mathematics, Vol. 29, No. 1, 1998, p. 73.

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A088515, A088516, A088546, A089545-A089552, A089554-A089558.

Programs

Mathematica

terms = 1000; jmax = 100; kmax = 200;
Reap[Do[If[CoprimeQ[j, k], e = j^2 - j k + k^2/2; f = j k; If[e > f, Sow[e^2 + f^2]]], {j, 1, jmax}, {k, 2, kmax, 2}]][[2, 1]] // Union // Take[#, terms]& (* Jean-François Alcover, Mar 04 2020 *)

Formula

a(n)=e^2+f^2, where e>f, e=j^2 - jk + k^2/2 and f=jk for coprime pairs (j, k) with k even.