[Fwd: SEQ+# A139490 FROM Artur Jasinski]

[Artur]

Could sombody explain some theory to this curious relation (to two bellow mentioned seq)

%I A139490
%S A139490 1, 4, 6, 7, 8, 10, 14, 16, 18
%N A139490 Numers k such that set of primes of the form x2+k x*y+y2 is that same as set of primes of the form x2+m y2 for some m
%e A139490 a(1)=1 because for k=1 set of primes is that same as m=3 other pairs {k,m}
a(2)={4,9}, a(3)={6,8}, a(4)={7,15}, a(5)={8,45}, a(6)={10,24}, a(7)={14,24}, a(8)={16,21}, a(9)={18,40}
%Y A139490 A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145
%O A139490 1
%K A139490 ,hard,more,nonn,
%A A139490 Artur Jasinski (grafix at csl.pl), Apr 24 2008

%I A139491
%S A139491 3, 8, 9, 15, 16, 21, 24, 40, 45, 48, 60
%N A139491 Numers m such that set primes of the form x2+m y2 are that same as set of primes of the form x2+k x*y+y2 for some k
%e A139491 a(1)=3 because for m=3 set of primes is that same as k=1 other pairs {m,k}:
a(2)={8,6}, a(3)={9,8}, a(4)={15,7}, a(5)={16,6}, a(6)={21,16}, a(7)={24,10 and 14}, a(8)={40,18}, a(9)={45,8}, a(10)={48,10} a(11)={60,8}
%Y A139491 A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145, A139490
%O A139491 1
%K A139491 ,hard,more,nonn,
%A A139491 Artur Jasinski (grafix at csl.pl), Apr 24 2008