Search: id:A035251
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%I A035251
%S A035251 1,2,4,7,8,9,14,16,17,18,23,25,28,31,32,34,36,41,46,47,49,50,56,62,63,
%T A035251 64,68,71,72,73,79,81,82,89,92,94,97,98,100,103,112,113,119,121,124,126,
%U A035251 127,128,136,137,142,144,146,151,153,158,161,162,164,167,169,175,178
%N A035251 Numbers of the form n = x^2-2y^2 with integers x, y.
%C A035251 n is representable in the form x^2-2y^2 iff every prime p == 3 or 5 mod 
               8 dividing n occurs to an even power.
%C A035251 Nonzero terms in expansion of Dirichlet series Product_p (1-(Kronecker(m,
               p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m= 2.
%C A035251 Also numbers of the form 2x^2 - y^2. If x^2 - 2y^2 = n, 2(x+y)^2 - (x+2y)^2 
               = n. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), 
               Nov 09 2009]
%H A035251 T. D. Noe, <a href="b035251.txt">Table of n, a(n) for n=1..1000</a>
%o A035251 (PARI) direuler(p=2,201,1/(1-(kronecker(2,p)*(X-X^2))-X))
%o A035251 (PARI) {a(n)= local(m, c); if(n<1, 0, c=0; m=0; while( c<n, m++; if( 
               sum(i=0, sqrtint(m\2), issquare(m+2*i^2)), c++)); m)} /* Michael 
               Somos Aug 17 2006 */
%Y A035251 Cf. A035185.
%Y A035251 Cf. A042965, A001481.
%Y A035251 Cf. A000047
%Y A035251 Sequence in context: A047351 A035248 A028951 this_sequence A141401 A132604 
               A013153
%Y A035251 Adjacent sequences: A035248 A035249 A035250 this_sequence A035252 A035253 
               A035254
%K A035251 nonn
%O A035251 1,2
%A A035251 N. J. A. Sloane (njas(AT)research.att.com).
%E A035251 Better description from Sharon Sela (sharonsela(AT)hotmail.com), Mar 
               10 2002

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