This site is supported by donations to The OEIS Foundation.



Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A264352 Exceptional even numbers D that do not admit a solution to the Pell equation X^2 - D Y^2 = +2. 3


%S 82,146,178,226,274,434,466,514,562,578,626,658,818,914,994,1042,1106,

%T 1138,1202,1234,1394,1426,1522,1582,1618,1666,1714,1778,1874,1906,

%U 1918,2066,2098,2162,2194,2258,2306,2386,2402,2434,2482,2578,2642

%N Exceptional even numbers D that do not admit a solution to the Pell equation X^2 - D Y^2 = +2.

%C These are the even numbers D = 2*d with odd d having no prime factors 3 or 5 (mod 8), and do not represent +2 by the indefinite binary quadratic form X^2 - D*Y^2 (with discriminant 4*D > 0).

%C These even D numbers satisfy the necessary condition given in A261246. This condition is not sufficient as the present numbers show.

%C a(n)/2 = d(n) is 7 (mod 8) for n = 24, 31, 48, 55, 57, ...

%C The numbers D which admit solutions to the Pell equation X^2 - D Y^2 = +2 are given by A261246.

%C The exceptional odd D numbers are given in A263010.

%Y Cf. A261246,A263010, A261247, A261248.

%K nonn

%O 1,1

%A _Wolfdieter Lang_, Nov 12 2015

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)