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 A088319 Ordered hypotenuses of primitive Pythagorean triangles having legs that add up to a square. 17
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 30 23:12 EDT 2021. Contains 346365 sequences. (Running on oeis4.)