The numbers k with k == 5 (mod 8), and s(k-2) = k with s(.) the hypothetical sequence generated by Turing Machine #4, are what I’ve called “b-numbers” for basic numbers.
I haven’t succeeded in finding any rule that determines the whole sequence. Below, I copy the 26 b-numbers below 256. I’ve found this to be a hard problem.
b-numbers below 256:
5
13
21
29
37
45
53
61
77
85
93
101
109
117
125
149
173
181
189
205
213
221
229
237
245
253
