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Second coordinate of fundamental unit of real quadratic field with discriminant A003658(n), n >= 2.
4

%I #29 Apr 14 2019 10:54:15

%S 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,

%T 1138,2,1,8,25,146,2,273,2968,15,6,298,1,16,2,5,6,4,17,1856,1,2,531,1,

%U 9384,97,3588,10,7,253970,2,72664,7,3,6440,5,521904,12,1,1,13

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

%C See A014000 for much more about this sequence. - _N. J. A. Sloane_, Jun 14 2013

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

%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Class number theory</a>

%H Steven R. Finch, <a href="/A000924/a000924.pdf">Class number theory</a> [Cached copy, with permission of the author]

%o (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

%Y Cf. A014000, A003658, A014077, A003652.

%K nonn

%O 2,5

%A Eric Rains (rains(AT)caltech.edu)

%E Offset corrected by _Jianing Song_, Mar 31 2019