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

1,1

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

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.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A297227 A089634 A142526 * A297598 A204620 A172085

Adjacent sequences: A088316 A088317 A088318 * A088320 A088321 A088322

Keyword

nonn

Author

Lekraj Beedassy, Nov 06 2003

Status

approved