Primary 3-bit (8 colors). Unique representation!

tput	hex
00	000000
01	800000
02	008000
03	808000
04	000080
05	800080
06	008080
07	c0c0c0

Equivalent "bright" versions of original 8 colors.

tput	hex
08	808080
09	ff0000
10	00ff00
11	ffff00
12	0000ff
13	ff00ff
14	00ffff
15	ffffff

Strictly ascending.

tput	hex
16	000000
17	00005f
18	000087
19	0000af
20	0000d7
21	0000ff
22	005f00
23	005f5f
24	005f87
25	005faf
26	005fd7
27	005fff
28	008700
29	00875f
30	008787
31	0087af
32	0087d7
33	0087ff
34	00af00
35	00af5f
36	00af87
37	00afaf
38	00afd7
39	00afff
40	00d700
41	00d75f
42	00d787
43	00d7af
44	00d7d7
45	00d7ff
46	00ff00
47	00ff5f
48	00ff87
49	00ffaf
50	00ffd7
51	00ffff
52	5f0000
53	5f005f
54	5f0087
55	5f00af
56	5f00d7
57	5f00ff
58	5f5f00
59	5f5f5f
60	5f5f87
61	5f5faf
62	5f5fd7
63	5f5fff
64	5f8700
65	5f875f
66	5f8787
67	5f87af
68	5f87d7
69	5f87ff
70	5faf00
71	5faf5f
72	5faf87
73	5fafaf
74	5fafd7
75	5fafff
76	5fd700
77	5fd75f
78	5fd787
79	5fd7af
80	5fd7d7
81	5fd7ff
82	5fff00
83	5fff5f
84	5fff87
85	5fffaf
86	5fffd7
87	5fffff
88	870000
89	87005f
90	870087
91	8700af
92	8700d7
93	8700ff
94	875f00
95	875f5f
96	875f87
97	875faf
98	875fd7
99	875fff
100	878700
101	87875f
102	878787
103	8787af
104	8787d7
105	8787ff
106	87af00
107	87af5f
108	87af87
109	87afaf
110	87afd7
111	87afff
112	87d700
113	87d75f
114	87d787
115	87d7af
116	87d7d7
117	87d7ff
118	87ff00
119	87ff5f
120	87ff87
121	87ffaf
122	87ffd7
123	87ffff
124	af0000
125	af005f
126	af0087
127	af00af
128	af00d7
129	af00ff
130	af5f00
131	af5f5f
132	af5f87
133	af5faf
134	af5fd7
135	af5fff
136	af8700
137	af875f
138	af8787
139	af87af
140	af87d7
141	af87ff
142	afaf00
143	afaf5f
144	afaf87
145	afafaf
146	afafd7
147	afafff
148	afd700
149	afd75f
150	afd787
151	afd7af
152	afd7d7
153	afd7ff
154	afff00
155	afff5f
156	afff87
157	afffaf
158	afffd7
159	afffff
160	d70000
161	d7005f
162	d70087
163	d700af
164	d700d7
165	d700ff
166	d75f00
167	d75f5f
168	d75f87
169	d75faf
170	d75fd7
171	d75fff
172	d78700
173	d7875f
174	d78787
175	d787af
176	d787d7
177	d787ff
178	d7af00
179	d7af5f
180	d7af87
181	d7afaf
182	d7afd7
183	d7afff
184	d7d700
185	d7d75f
186	d7d787
187	d7d7af
188	d7d7d7
189	d7d7ff
190	d7ff00
191	d7ff5f
192	d7ff87
193	d7ffaf
194	d7ffd7
195	d7ffff
196	ff0000
197	ff005f
198	ff0087
199	ff00af
200	ff00d7
201	ff00ff
202	ff5f00
203	ff5f5f
204	ff5f87
205	ff5faf
206	ff5fd7
207	ff5fff
208	ff8700
209	ff875f
210	ff8787
211	ff87af
212	ff87d7
213	ff87ff
214	ffaf00
215	ffaf5f
216	ffaf87
217	ffafaf
218	ffafd7
219	ffafff
220	ffd700
221	ffd75f
222	ffd787
223	ffd7af
224	ffd7d7
225	ffd7ff
226	ffff00
227	ffff5f
228	ffff87
229	ffffaf
230	ffffd7
231	ffffff

Gray-scale range.

tput	hex
232	080808
233	121212
234	1c1c1c
235	262626
236	303030
237	3a3a3a
238	444444
239	4e4e4e
240	585858
241	626262
242	6c6c6c
243	767676
244	808080
245	8a8a8a
246	949494
247	9e9e9e
248	a8a8a8
249	b2b2b2
250	bcbcbc
251	c6c6c6
252	d0d0d0
253	dadada
254	e4e4e4
255	eeeeee