Deadfish/Constants

Given below are the shortest ways to produce a number in the range of 0 to 289 with Deadfish. At most 38 instructions are necessary to reach from 0 to any number in that range. 
The shortest way to reach any number is to generate the instructions from right to left by adding i/ds from the nearest square, add an s, then continue isolating recursively until 0 to 3 are reached, which are then generated via is alone. 3 is included since it would otherwise be generated as iisd - its nearest square is 4.
For example, the code for 33 generates as such:
 
 ddd nearest square
 sddd square root
 iisddd nearest square
siisddd square root
 iisiisddd ii
For numbers above 240, we theorize the same method holds, except for a couple caveats:
* The nearest valid square in the range 241 to 272 is no longer 256. Numbers below would lead to 225 = 15², and numbers above would lead to 289 = 17².
* Any squares involving 256 should be avoided.
* 65537 = 256² + 1 needs to go via 255² rather than 257² - they're the same distance, but the former is itself shorter.
== List of Deadfish constants ==
0 = 
1 = i
2 = ii
3 = iii
4 = iis
5 = iisi
6 = iisii
7 = iiisdd
8 = iiisd
9 = iiis
10 = iiisi
11 = iiisii
12 = iiisiii
13 = iissddd
14 = iissdd
15 = iissd
16 = iiss
17 = iissi
18 = iissii
19 = iissiii
20 = iissiiii
21 = iisisdddd
22 = iisisddd
23 = iisisdd
24 = iisisd
25 = iisis
26 = iisisi
27 = iisisii
28 = iisisiii
29 = iisisiiii
30 = iisisiiiii
31 = iisiisddddd
32 = iisiisdddd
33 = iisiisddd
34 = iisiisdd
35 = iisiisd
36 = iisiis
37 = iisiisi
38 = iisiisii
39 = iisiisiii
40 = iisiisiiii
41 = iisiisiiiii
42 = iisiisiiiiii
43 = iiisddsdddddd
44 = iiisddsddddd
45 = iiisddsdddd
46 = iiisddsddd
47 = iiisddsdd
48 = iiisddsd
49 = iiisdds
50 = iiisddsi
51 = iiisddsii
52 = iiisddsiii
53 = iiisddsiiii
54 = iiisddsiiiii
55 = iiisddsiiiiii
56 = iiisddsiiiiiii
57 = iiisdsddddddd
58 = iiisdsdddddd
59 = iiisdsddddd
60 = iiisdsdddd
61 = iiisdsddd
62 = iiisdsdd
63 = iiisdsd
64 = iiisds
65 = iiisdsi
66 = iiisdsii
67 = iiisdsiii
68 = iiisdsiiii
69 = iiisdsiiiii
70 = iiisdsiiiiii
71 = iiisdsiiiiiii
72 = iiisdsiiiiiiii
73 = iiissdddddddd
74 = iiissddddddd
75 = iiissdddddd
76 = iiissddddd
77 = iiissdddd
78 = iiissddd
79 = iiissdd
80 = iiissd
81 = iiiss
82 = iiissi
83 = iiissii
84 = iiissiii
85 = iiissiiii
86 = iiissiiiii
87 = iiissiiiiii
88 = iiissiiiiiii
89 = iiissiiiiiiii
90 = iiissiiiiiiiii
91 = iiisisddddddddd
92 = iiisisdddddddd
93 = iiisisddddddd
94 = iiisisdddddd
95 = iiisisddddd
96 = iiisisdddd
97 = iiisisddd
98 = iiisisdd
99 = iiisisd
100 = iiisis
101 = iiisisi
102 = iiisisii
103 = iiisisiii
104 = iiisisiiii
105 = iiisisiiiii
106 = iiisisiiiiii
107 = iiisisiiiiiii
108 = iiisisiiiiiiii
109 = iiisisiiiiiiiii
110 = iiisisiiiiiiiiii
111 = iiisiisdddddddddd
112 = iiisiisddddddddd
113 = iiisiisdddddddd
114 = iiisiisddddddd
115 = iiisiisdddddd
116 = iiisiisddddd
117 = iiisiisdddd
118 = iiisiisddd
119 = iiisiisdd
120 = iiisiisd
121 = iiisiis
122 = iiisiisi
123 = iiisiisii
124 = iiisiisiii
125 = iiisiisiiii
126 = iiisiisiiiii
127 = iiisiisiiiiii
128 = iiisiisiiiiiii
129 = iiisiisiiiiiiii
130 = iiisiisiiiiiiiii
131 = iiisiisiiiiiiiiii
132 = iiisiisiiiiiiiiiii
133 = iiisiiisddddddddddd
134 = iiisiiisdddddddddd
135 = iiisiiisddddddddd
136 = iiisiiisdddddddd
137 = iiisiiisddddddd
138 = iiisiiisdddddd
139 = iiisiiisddddd
140 = iiisiiisdddd
141 = iiisiiisddd
142 = iiisiiisdd
143 = iiisiiisd
144 = iiisiiis
145 = iiisiiisi
146 = iiisiiisii
147 = iiisiiisiii
148 = iiisiiisiiii
149 = iiisiiisiiiii
150 = iiisiiisiiiiii
151 = iiisiiisiiiiiii
152 = iiisiiisiiiiiiii
153 = iiisiiisiiiiiiiii
154 = iiisiiisiiiiiiiiii
155 = iiisiiisiiiiiiiiiii
156 = iiisiiisiiiiiiiiiiii
157 = iissdddsdddddddddddd
158 = iissdddsddddddddddd
159 = iissdddsdddddddddd
160 = iissdddsddddddddd
161 = iissdddsdddddddd
162 = iissdddsddddddd
163 = iissdddsdddddd
164 = iissdddsddddd
165 = iissdddsdddd
166 = iissdddsddd
167 = iissdddsdd
168 = iissdddsd
169 = iissddds
170 = iissdddsi
171 = iissdddsii
172 = iissdddsiii
173 = iissdddsiiii
174 = iissdddsiiiii
175 = iissdddsiiiiii
176 = iissdddsiiiiiii
177 = iissdddsiiiiiiii
178 = iissdddsiiiiiiiii
179 = iissdddsiiiiiiiiii
180 = iissdddsiiiiiiiiiii
181 = iissdddsiiiiiiiiiiii
182 = iissdddsiiiiiiiiiiiii
183 = iissddsddddddddddddd
184 = iissddsdddddddddddd
185 = iissddsddddddddddd
186 = iissddsdddddddddd
187 = iissddsddddddddd
188 = iissddsdddddddd
189 = iissddsddddddd
190 = iissddsdddddd
191 = iissddsddddd
192 = iissddsdddd
193 = iissddsddd
194 = iissddsdd
195 = iissddsd
196 = iissdds
197 = iissddsi
198 = iissddsii
199 = iissddsiii
200 = iissddsiiii
201 = iissddsiiiii
202 = iissddsiiiiii
203 = iissddsiiiiiii
204 = iissddsiiiiiiii
205 = iissddsiiiiiiiii
206 = iissddsiiiiiiiiii
207 = iissddsiiiiiiiiiii
208 = iissddsiiiiiiiiiiii
209 = iissddsiiiiiiiiiiiii
210 = iissddsiiiiiiiiiiiiii
211 = iissdsdddddddddddddd
212 = iissdsddddddddddddd
213 = iissdsdddddddddddd
214 = iissdsddddddddddd
215 = iissdsdddddddddd
216 = iissdsddddddddd
217 = iissdsdddddddd
218 = iissdsddddddd
219 = iissdsdddddd
220 = iissdsddddd
221 = iissdsdddd
222 = iissdsddd
223 = iissdsdd
224 = iissdsd
225 = iissds
226 = iissdsi
227 = iissdsii
228 = iissdsiii
229 = iissdsiiii
230 = iissdsiiiii
231 = iissdsiiiiii
232 = iissdsiiiiiii
233 = iissdsiiiiiiii
234 = iissdsiiiiiiiii
235 = iissdsiiiiiiiiii
236 = iissdsiiiiiiiiiii
237 = iissdsiiiiiiiiiiii
238 = iissdsiiiiiiiiiiiii
239 = iissdsiiiiiiiiiiiiii
240 = iissdsiiiiiiiiiiiiiii
241 = iissdsiiiiiiiiiiiiiiii
242 = iissdsiiiiiiiiiiiiiiiii
243 = iissdsiiiiiiiiiiiiiiiiii
244 = iissdsiiiiiiiiiiiiiiiiiii
245 = iissdsiiiiiiiiiiiiiiiiiiii
246 = iissdsiiiiiiiiiiiiiiiiiiiii
247 = iissdsiiiiiiiiiiiiiiiiiiiiii
248 = iissdsiiiiiiiiiiiiiiiiiiiiiii
249 = iissdsiiiiiiiiiiiiiiiiiiiiiiii
250 = iissdsiiiiiiiiiiiiiiiiiiiiiiiii
251 = iissdsiiiiiiiiiiiiiiiiiiiiiiiiii
252 = iissdsiiiiiiiiiiiiiiiiiiiiiiiiiii
253 = iissdsiiiiiiiiiiiiiiiiiiiiiiiiiiii
254 = iissdsiiiiiiiiiiiiiiiiiiiiiiiiiiiii
255 = iissdsiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
257 = iissisdddddddddddddddddddddddddddddddd
258 = iissisddddddddddddddddddddddddddddddd
259 = iissisdddddddddddddddddddddddddddddd
260 = iissisddddddddddddddddddddddddddddd
261 = iissisdddddddddddddddddddddddddddd
262 = iissisddddddddddddddddddddddddddd
263 = iissisdddddddddddddddddddddddddd
264 = iissisddddddddddddddddddddddddd
265 = iissisdddddddddddddddddddddddd
266 = iissisddddddddddddddddddddddd
267 = iissisdddddddddddddddddddddd
268 = iissisddddddddddddddddddddd
269 = iissisdddddddddddddddddddd
270 = iissisddddddddddddddddddd
271 = iissisdddddddddddddddddd
272 = iissisddddddddddddddddd
273 = iissisdddddddddddddddd
274 = iissisddddddddddddddd
275 = iissisdddddddddddddd
276 = iissisddddddddddddd
277 = iissisdddddddddddd
278 = iissisddddddddddd
279 = iissisdddddddddd
280 = iissisddddddddd
281 = iissisdddddddd
282 = iissisddddddd
283 = iissisdddddd
284 = iissisddddd
285 = iissisdddd
286 = iissisddd
287 = iissisdd
288 = iissisd
289 = iissis
290 = iissisi
== Links ==
* Haskell program to generate the constants up to 255
Category:Examples