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A088241 Values of y, where x^2 + xy + y^2 = p (x is a prime of the form 6n + 1 (A002476).

%I A088241 #15 Jun 16 2025 15:04:02
%S A088241 2,3,3,5,4,6,5,7,8,7,8,9,7,7,10,9,12,11,11,9,13,14,11,12,15,10,12,13,
%T A088241 17,16,11,13,17,13,17,15,12,15,20,13,18,17,21,21,18,17,21,14,21,19,24,
%U A088241 23,19,22,15,18,20,21,19,25,18,19,23,21,27,17,27,25,19,20,27,23,28,21,26
%N A088241 Values of y, where x^2 + xy + y^2 = p (x<y) is a prime of the form 6n + 1 (A002476).
%H A088241 Robert Israel, <a href="/A088241/b088241.txt">Table of n, a(n) for n = 1..10000</a>
%p A088241 R:= NULL: count:= 0:
%p A088241 for k from 1 while count < 100 do
%p A088241   p:= 6*k+1;
%p A088241   if not isprime(p) then next fi;
%p A088241   S:= select(t -> subs(t,x) > 0 and subs(t,x) < subs(t,y), [isolve(x^2+x*y+y^2=p)]);
%p A088241   S:= map(t -> subs(t,y), S);
%p A088241   R:= R,op(S); count:= count+1;
%p A088241 od:
%p A088241 R; #_Robert Israel_, Jun 16 2025
%t A088241 Reap[For[n = 1, n <= 200, n++, If[PrimeQ[p = 6 n + 1], s = Solve[x^2 + x y + y^2 == p && 0 < x < y, {x, y}, Integers]; Sow[y /. s[[1]]]]]][[2, 1]] (* _Jean-François Alcover_, Mar 07 2020 *)
%Y A088241 Cf. A002476, A088242, A088243, A088296, A088298, A088299, A088977.
%K A088241 nonn
%O A088241 1,1
%A A088241 _Lekraj Beedassy_, Nov 03 2003
%E A088241 More terms from _Ray Chandler_, Nov 04 2003