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 A014000 First coordinate of fundamental unit of real quadratic field. 5
 0, 1, 2, 1, 3, 2, 5, 8, 2, 19, 5, 3, 27, 10, 3, 15, 131, 4, 17, 7, 11, 943, 170, 4, 4, 197, 447, 24, 13, 5035, 9, 5, 37, 118, 703, 11, 1520, 15371, 79, 35, 1595, 6, 87, 11, 28, 37, 25, 98, 10847, 6, 13, 3482, 6, 57731, 604, 24335, 63, 48, 1637147, 13, 478763 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Taken from Cohen's table on pages 515-519. The table is indexed by the discriminant d = d(K) = A003658(n) of the real quadratic fields K. The fundamental unit is given as a pair of coordinates (a,b) = (A014000(n), A014046(n)) expressed in terms of the canonical integral basis (1,w) where w = (1+sqrt(d))/2 if d == 1 mod 4, w = sqrt(d)/2 if d == 0 mod 4. The norm of this fundamental unit is A014077(n). The class number h(K) is A003652(n). - N. J. A. Sloane, Jun 14 2013 REFERENCES H. Cohen, A Course in Computational Alg. No. Theory, Springer, 1993, p. 515-519. LINKS S. R. Finch, Class number theory [Cached copy, with permission of the author] Keith Matthews, Finding the fundamental unit of a real quadratic field EXAMPLE Here is the start of Cohen's list of fundamental units: [0, 1], [1, 1], [2, 1], [1, 1], [3, 2], [2, 1], [5, 2], [8, 3], [2, 1], [19, 8], [5, 2], [3, 1], [27, 10], [10, 3], [3, 1], [15, 4], [131, 40],[4, 1], [17, 5], [7, 2], [11, 3], [943, 250], [170, 39], [4, 1], [4, 1], [197, 42], [447, 106], [24, 5], [13, 3], [5035, 1138], [9, 2], [5, 1], [37, 8], [118, 25], [703, 146], [11, 2], [1520, 273], [15371, 2968], [79, 15], [35, 6], [1595, 298], [6, 1], [87, 16], [11, 2], [28, 5], [37, 6], [25, 4], [98, 17], [10847, 1856], [6, 1], [13, 2], [3482, 531], [6, 1], [57731, 9384], [604, 97], [24335, 3588], [63, 10], [48, 7], [1637147, 253970], [13, 2], [478763, 72664], ... [N. J. A. Sloane, Jun 14 2013] CROSSREFS Cf. A014046, A003658, A014077, A003652. Sequence in context: A145794 A176741 A266138 * A075257 A260618 A226651 Adjacent sequences:  A013997 A013998 A013999 * A014001 A014002 A014003 KEYWORD nonn AUTHOR Eric Rains (rains(AT)caltech.edu) EXTENSIONS Edited by N. J. A. Sloane, Jun 14 2013 STATUS approved

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Last modified January 16 19:49 EST 2019. Contains 319206 sequences. (Running on oeis4.)