A033682 - OEIS

%I #19 Nov 19 2022 01:15:19

%S 25,65,125,169,205,305,325,425,533,565,625,725,793,905,1025,1105,1325,

%T 1469,1525,1565,1681,1825,1885,2105,2125,2353,2405,2501,2725,2825,

%U 2873,3065,3425,3445,3485,3625

%N Numbers of the form (q^2+(q+1)^2)*(r^2+(r+1)^2), q,r >= 1.

%C All terms == 1,3,5 or 9 (mod 10). - _Robert Israel_, Mar 20 2018

%D G. Tenenbaum, pp. 268ff of R. L. Graham et al., eds., Mathematics of Paul Erdős I.

%H Robert Israel, <a href="/A033682/b033682.txt">Table of n, a(n) for n = 1..10000</a>

%p N:= 10000: # to get all terms <= N

%p g:= n -> n^2+(n+1)^2:

%p sort(convert({seq(seq(g(q)*g(r), r = 1 .. floor((sqrt(2*N/g(q)-1)-1)/2)), q=1 .. floor((sqrt(2*N/5-1)-1)/2))},list)); # _Robert Israel_, Mar 20 2018

%t With[{nn=30},Select[Union[Flatten[Table[(q^2+(q+1)^2)(r^2+(r+1)^2),{q,nn},{r,q}]]],#<=5(nn^2+(nn+1)^2)&]] (* _Harvey P. Dale_, Jan 28 2019 *)

%K nonn

%O 1,1

%A _N. J. A. Sloane_