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Search: id:A088319
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| A088319 |
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Ordered hypotenuses of primitive Pythagorean triangles having legs that add up to a square. |
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17
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| 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; listen)
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OFFSET
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1,1
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REFERENCES
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F. Rubin, "Squared" Pythagorean Triples, Solution to problem 2306, J. Recreational Mathematics, Vol. 29, No. 1, 1998, p. 73.
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FORMULA
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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.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A088515, A088516, A089545-A089558.
Sequence in context: A141939 A089634 A142526 this_sequence A142392 A142943 A142183
Adjacent sequences: A088316 A088317 A088318 this_sequence A088320 A088321 A088322
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Nov 06 2003
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