|
%I #13 Jan 13 2013 12:44:57
%S 6,9,14,21,46,49,69,86,94,129,134,141,145,161,166,201,205,206,214,249,
%T 254,301,305,309,321,326,329,334,381,445,446,454,469,489,501,505,526,
%U 529,545,566,581,614,669,681,694,721,734,745,749,766,789,841,849,886,889
%N Semiprimes that can be written in the form x^2 + 5*y^2 with x, y > 0.
%C If two primes which end in 3 or 7 and surpass by 3 a multiple of 4 are multiplied, then their product will be composed of a square and the quintuple of another square. (Fermat (1654))
%D Dedekind R., Theory of Algebraic Integers, Cambridge Univ. Press, 1996 (translation of the 1877 French original), pp. 12-13.
%H Arkadiusz Wesolowski, <a href="/A218697/b218697.txt">Table of n, a(n) for n = 1..10000</a>
%F A154778 INTERSECT A001358.
%e 94 = 7^2 + 5*3^2, therefore 94 is a term.
%t n = 889; limx = Sqrt[n]; limy = Sqrt[n/5]; Select[Union@Flatten@Table[x^2 + 5*y^2, {x, limx}, {y, limy}], # <= n && PrimeOmega[#] == 2 &]
%t Select[Select[Range[889], PrimeOmega[#] == 2 &], Length@FindInstance[y > 0 && x^2 + 5*y^2 == #, {x, y}, Integers] > 0 &] (* _Arkadiusz Wesolowski_, Jan 13 2013 *)
%Y Cf. A001358, A154778.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Nov 04 2012
|
