2,5

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

From Jianing Song, Mar 22 2026: (Start)

If (x0,y0) is the smallest positive solution to x^2 - D*y^2 = +-4, D = A003658(n), then a(n) = y0. Note that A014000(n) = x_0/2 if D == 0 (mod 4), (x_0-y_0)/2 if D == 1 (mod 4).

Let K be the real quadratic field of discriminant A003658(n). Then a(n) is the index in O_K of the quadratic order generated by units in O_K. (End)

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

Jianing Song, Table of n, a(n) for n = 2..10000

S. R. Finch, Class number theory

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

(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

(PARI) for(D=2, 200, if(isfundamental(D), print1(imag(quadunit(D)), ", "))) \\ Jianing Song, Mar 22 2026

Cf. A014000, A003658, A014077, A003652, A393497 (index of the quadratic order generated by units of norm 1).

Sequence in context: A334550 A232177 A111377 * A384147 A243919 A231775

Adjacent sequences: A014043 A014044 A014045 * A014047 A014048 A014049

Eric Rains (rains(AT)caltech.edu)

Offset corrected by Jianing Song, Mar 31 2019

approved