cp's OEIS Frontend

A229769 Not of the form x^2 + P*y^2 for integers x > 0, y > 1, P a prime.

%I A229769 #5 Sep 30 2013 19:22:57
%S A229769 1,2,3,4,5,6,7,8,10,11,14,15,18,20,23,25,26,30,35,38,39,40,42,47,50,
%T A229769 55,58,62,65,71,74,78,83,87,90,95,98,106,110,119,122,130,138,143,146,
%U A229769 155,158,159,167,170,182,186,190,195,203,210,215,218,222,227,230,231,250
%N A229769 Not of the form x^2 + P*y^2 for integers x > 0, y > 1, P a prime.
%C A229769 There are no terms <= 10^9 greater than a(3036) = 69808035, leading to the conjecture that the sequence is finite. If true, every sufficiently large number is expressible as x^2 + P*y^2 with x > 0, y > 1.
%H A229769 Chris Boyd, <a href="/A229769/b229769.txt">Table of n, a(n) for n = 1..3036</a>
%e A229769 Since 17 can be expressed as 3^2 + 2 * 2^2, it is not in the sequence.
%e A229769 No such expression exists for 18, hence it is in the sequence.
%e A229769 Since 19 can be expressed as 1^2 + 2 * 3^2, it is not in the sequence.
%o A229769 (PARI) test(n)={local(z,x,p,y);for(x=1,sqrtint(n),z=n-x^2;p=core(z);y=core(z,1)[2];if(isprime(p)&&y>1,return(1)));}
%o A229769 for(n=1,300,if(test(n)==0,print1(n",")))
%Y A229769 Supersequence of A074885 (x^2 + M*y^2, x > 0, y > 1, M > 0).
%Y A229769 Supersequence of A212709 (not of the form p*c^2 + b^2, with p prime and c and b nonzero integers).
%K A229769 nonn
%O A229769 1,2
%A A229769 _Chris Boyd_, Sep 29 2013