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

1,4

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.

Links

Table of n, a(n) for n=1..51.

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

Example

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,
...

Crossrefs

Cf. A349810.

Sequence in context: A019130 A245348 A174551 * A239799 A305235 A120011

Adjacent sequences: A349808 A349809 A349810 * A349812 A349813 A349814

Keyword

nonn,tabf

Author

N. J. A. Sloane, Dec 22 2021

Status

approved