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A096033
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Difference between leg and hypotenuse in primitive Pythagorean triangles.
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7
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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
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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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.
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FORMULA
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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
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MATHEMATICA
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nmax = 100;
Union[2 Range[nmax]^2, (2 Range[0, Ceiling[nmax/Sqrt[2]]] + 1)^2] (* Jean-François Alcover, Jan 01 2019 *)
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PROG
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(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
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CROSSREFS
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Cf. A001105, A004641, A016754, A094904, A245058.
Sequence in context: A033492 A126160 A118962 * A073413 A046681 A259672
Adjacent sequences: A096030 A096031 A096032 * A096034 A096035 A096036
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KEYWORD
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nonn,easy
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AUTHOR
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Lekraj Beedassy, Jun 16 2004
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EXTENSIONS
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Corrected and extended by Matthew Vandermast and Ray Chandler, Jun 17 2004
Erroneous comment deleted by Andrew Weimholt, Sep 07 2010
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STATUS
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approved
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