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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
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
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
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