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Search: id:A035251
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| A035251 |
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Numbers of the form n = x^2-2y^2 with integers x, y. |
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+0
8
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| 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, 64, 68, 71, 72, 73, 79, 81, 82, 89, 92, 94, 97, 98, 100, 103, 112, 113, 119, 121, 124, 126, 127, 128, 136, 137, 142, 144, 146, 151, 153, 158, 161, 162, 164, 167, 169, 175, 178
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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.
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]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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PROGRAM
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(PARI) direuler(p=2, 201, 1/(1-(kronecker(2, p)*(X-X^2))-X))
(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 */
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CROSSREFS
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Cf. A035185.
Cf. A042965, A001481.
Cf. A000047
Sequence in context: A047351 A035248 A028951 this_sequence A141401 A132604 A013153
Adjacent sequences: A035248 A035249 A035250 this_sequence A035252 A035253 A035254
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KEYWORD
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nonn,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Better description from Sharon Sela (sharonsela(AT)hotmail.com), Mar 10 2002
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