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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.

%I A349811 #9 Dec 23 2021 12:08:32
%S A349811 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,
%T A349811 40,17,29,12,5,5401,2190,888,324,126,49,14,5,2,22,8,3,1705,618,224,
%U A349811 793,283,101,2166673601,761875860,267901370
%N 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.
%C A349811 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.
%C A349811 Wada's table extends to m=249.
%H A349811 Hideo Wada, <a href="https://doi.org/10.3792/pja/1195526509">A table of fundamental units of purely cubic fields</a>, Proc. Japan Acad. 46 (1970), 1135-1140. [Math. Rev. MR0294292]
%e A349811 The table begins as follows (the denominator d has been included if it is not 1, and m = A349810(n)):
%e A349811 n  m  (T(n,0) T(n,1) T(n,2))/d
%e A349811 1  2  1, 1, 1,
%e A349811 2  3  4, 3, 2,
%e A349811 3  5  41, 24, 14,
%e A349811 4  6  109, 60, 33,
%e A349811 5  7  4, 2, 1,
%e A349811 6 10  (23, 11, 5)/3,
%e A349811 7 11  89, 40, 18,
%e A349811 8 12  (110, 48, 21)/2,
%e A349811 9 13  94, 40, 17,
%e A349811 10 14 29, 12, 5,
%e A349811 11 15 5401, 2190, 888,
%e A349811 12 17 324, 126, 49,
%e A349811 13 19 (14, 5, 2)/3,
%e A349811 14 20 (22, 8, 3)/2,
%e A349811 15 21 1705, 618, 224,
%e A349811 16 22 793, 283, 101,
%e A349811 17 23 2166673601, 761875860, 267901370,
%e A349811 ...
%Y A349811 Cf. A349810.
%K A349811 nonn,tabf
%O A349811 1,4
%A A349811 _N. J. A. Sloane_, Dec 22 2021