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 A096033 Difference between leg and hypotenuse in primitive Pythagorean triangles. 7
 1, 2, 8, 9, 18, 25, 32, 49, 50, 72, 81, 98, 121, 128, 162, 169, 200, 225, 242, 288, 289, 338, 361, 392, 441, 450, 512, 529, 578, 625, 648, 722, 729, 800, 841, 882, 961, 968, 1058, 1089, 1152, 1225, 1250, 1352, 1369, 1458, 1521, 1568, 1681, 1682, 1800, 1849 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Consists of the odd squares and the halves of the even squares. - Andrew Weimholt, Sep 07 2010 Question: Do we have a(n) mod 2 = A004641(n)? - David A. Corneth, Jan 02 2019 REFERENCES L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 170. LINKS David A. Corneth, Table of n, a(n) for n = 1..10099 James M. Parks, Computing Pythagorean Triples, arXiv:2107.06891 [math.GM], 2021. James M. Parks, On the Curved Patterns Seen in the Graph of PPTs, arXiv:2104.09449 [math.CO], 2021. FORMULA Union of A001105 (integers of form 2*n^2) and A016754 (the odd squares). Sum_{n>=1} 1/a(n) = 5*Pi^2/24 = 10 * A245058. - Amiram Eldar, Feb 14 2021 MATHEMATICA nmax = 100; Union[2 Range[nmax]^2, (2 Range[0, Ceiling[nmax/Sqrt[2]]] + 1)^2] (* Jean-François Alcover, Jan 01 2019 *) PROG (PARI) upto(n) = vecsort(concat(vector((sqrtint(n)+1)\2, i, (2*i-1)^2), vector(sqrtint(n\2), i, 2*i^2))) \\ David A. Corneth, Jan 02 2019 CROSSREFS Cf. A001105, A004641, A016754, A094904, A245058. Sequence in context: A033492 A126160 A118962 * A073413 A046681 A259672 Adjacent sequences: A096030 A096031 A096032 * A096034 A096035 A096036 KEYWORD nonn,easy AUTHOR Lekraj Beedassy, Jun 16 2004 EXTENSIONS Corrected and extended by Matthew Vandermast and Ray Chandler, Jun 17 2004 Erroneous comment deleted by Andrew Weimholt, Sep 07 2010 STATUS approved

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Last modified March 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)