A014046 Second coordinate of fundamental unit of real quadratic field with discriminant A003658(n), n >= 2.

1, 1, 1, 1, 2, 1, 2, 3, 1, 8, 2, 1, 10, 3, 1, 4, 40, 1, 5, 2, 3, 250, 39, 1, 1, 42, 106, 5, 3, 1138, 2, 1, 8, 25, 146, 2, 273, 2968, 15, 6, 298, 1, 16, 2, 5, 6, 4, 17, 1856, 1, 2, 531, 1, 9384, 97, 3588, 10, 7, 253970, 2, 72664, 7, 3, 6440, 5, 521904, 12, 1, 1, 13

Offset: 2

Author

Eric Rains (rains(AT)caltech.edu)

Keywords

• nonn

Comments

See A014000 for much more about this sequence. - N. J. A. Sloane, Jun 14 2013

References

• H. Cohen, A Course in Computational Algebraic Number Theory, Springer, 1993, pp. 515-519.

Links

• S. R. Finch, Class number theory
• Steven R. Finch, Class number theory [Cached copy, with permission of the author]

Crossrefs

Cf. A014000, A003658, A014077, A003652.

Programs

PARI

lista(nn) = { for (n=2, nn, if (isfundamental(n), nc = core(n); m = Mod (nc, 4); if ((m == 2) || (m == 3), d = 1); if ((m == 1), d = 4); b = 1; a = 0; while (a == 0, v = nc*b^2; if (issquare(v-d), a = sqrtint(v-d), if (issquare(v+d), a = sqrtint(v+d))); if (a == 0, b++; );); print1(b, ", ");););} \\ Michel Marcus, Sep 25 2018

Extensions

Offset corrected by Jianing Song, Mar 31 2019