A349811 Table of triples read by rows: the fundamental unit of the purely real cubic field Q(m^(1/3)), m = A349810(n), is (T(n,0) + T(n,1)*x + T(n,2)*x^2)/d, where x = m^(1/3) and d is a small integer, usually 1.

1, 1, 1, 4, 3, 2, 41, 24, 14, 109, 60, 33, 4, 2, 1, 23, 11, 5, 89, 40, 18, 110, 48, 21, 94, 40, 17, 29, 12, 5, 5401, 2190, 888, 324, 126, 49, 14, 5, 2, 22, 8, 3, 1705, 618, 224, 793, 283, 101, 2166673601, 761875860, 267901370

Offset: 1

Author

N. J. A. Sloane, Dec 22 2021

Keywords

• nonn
• tabf

Comments

The denominator d is 1 with the following exceptions: 3 for m=10, 2 for m=12, 3 for m=19, 2 for m=20, and so on.

Wada's table extends to m=249.

Examples

			The table begins as follows (the denominator d has been included if it is not 1, and m = A349810(n)):
n  m  (T(n,0) T(n,1) T(n,2))/d
1  2  1, 1, 1,
2  3  4, 3, 2,
3  5  41, 24, 14,
4  6  109, 60, 33,
5  7  4, 2, 1,
6 10  (23, 11, 5)/3,
7 11  89, 40, 18,
8 12  (110, 48, 21)/2,
9 13  94, 40, 17,
10 14 29, 12, 5,
11 15 5401, 2190, 888,
12 17 324, 126, 49,
13 19 (14, 5, 2)/3,
14 20 (22, 8, 3)/2,
15 21 1705, 618, 224,
16 22 793, 283, 101,
17 23 2166673601, 761875860, 267901370,
...
		

Links

• Hideo Wada, A table of fundamental units of purely cubic fields, Proc. Japan Acad. 46 (1970), 1135-1140. [Math. Rev. MR0294292]

Crossrefs

Cf. A349810.