A264352 Exceptional even numbers D that do not admit a solution to the Pell equation X^2 - D Y^2 = +2.

82, 146, 178, 226, 274, 434, 466, 514, 562, 578, 626, 658, 818, 914, 994, 1042, 1106, 1138, 1202, 1234, 1394, 1426, 1522, 1582, 1618, 1666, 1714, 1778, 1874, 1906, 1918, 2066, 2098, 2162, 2194, 2258, 2306, 2386, 2402, 2434, 2482, 2578, 2642

Offset: 1

Author

Wolfdieter Lang, Nov 12 2015

Keywords

• nonn

Comments

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).

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

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

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

The exceptional odd D numbers are given in A263010.

Crossrefs

Cf. A261246,A263010, A261247, A261248.