Deadfish/Constants

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Given below are the shortest ways to produce a number in the range of 0 to 255 with Deadfish. At most 36 instructions are necessary to reach any number in that range.

The shortest way to reach any number is generally to produce the nearest square possible (256 is impossible) and then increment/decrement from there. Decrement/increment to the nearest square, add the square instruction and then recurse with the nearest square, with the exception of the numbers 0 to 3, which are shorter by just using increments without squaring and/or recursion. Otherwise, 3 would become iisd because the nearest square of 3 is 4.

For numbers above 256 we theorize the same method holds, except for a couple caveats:

  • 257 needs to go via 289 = 17² rather than the equally close 225 = 15², since the latter would require passing through the impossible 256.
  • The expensive square 65536 = 256² should be avoided, going via either 255² or 257² instead.
  • 65537 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

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