|
%I #44 Jul 23 2021 02:17:29
%S 1,2,8,9,18,25,32,49,50,72,81,98,121,128,162,169,200,225,242,288,289,
%T 338,361,392,441,450,512,529,578,625,648,722,729,800,841,882,961,968,
%U 1058,1089,1152,1225,1250,1352,1369,1458,1521,1568,1681,1682,1800,1849
%N Difference between leg and hypotenuse in primitive Pythagorean triangles.
%C Consists of the odd squares and the halves of the even squares. - _Andrew Weimholt_, Sep 07 2010
%C Question: Do we have a(n) mod 2 = A004641(n)? - _David A. Corneth_, Jan 02 2019
%D 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.
%H David A. Corneth, <a href="/A096033/b096033.txt">Table of n, a(n) for n = 1..10099</a>
%H James M. Parks, <a href="https://arxiv.org/abs/2107.06891">Computing Pythagorean Triples</a>, arXiv:2107.06891 [math.GM], 2021.
%H James M. Parks, <a href="https://arxiv.org/abs/2104.09449">On the Curved Patterns Seen in the Graph of PPTs</a>, arXiv:2104.09449 [math.CO], 2021.
%F Union of A001105 (integers of form 2*n^2) and A016754 (the odd squares).
%F Sum_{n>=1} 1/a(n) = 5*Pi^2/24 = 10 * A245058. - _Amiram Eldar_, Feb 14 2021
%t nmax = 100;
%t Union[2 Range[nmax]^2, (2 Range[0, Ceiling[nmax/Sqrt[2]]] + 1)^2] (* _Jean-François Alcover_, Jan 01 2019 *)
%o (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
%Y Cf. A001105, A004641, A016754, A094904, A245058.
%K nonn,easy
%O 1,2
%A _Lekraj Beedassy_, Jun 16 2004
%E Corrected and extended by _Matthew Vandermast_ and _Ray Chandler_, Jun 17 2004
%E Erroneous comment deleted by _Andrew Weimholt_, Sep 07 2010
|
