[seqfan] Stacking binary blocks 100, 010, 001, 111

[mail at fumba.eu]

Dear Seqfans,

While ordering a large matrix of "binary blocks" (see below, and  
without going into technical details of why I was actually doing  
that), it appeared I'd stumbled on the sequence A047541 (Numbers that  
are congruent to {1, 2, 4, 7} mod 8) and I was happy to see the  
explicit formula. However, these are not the same- the first deviation  
appears on the 13th term. Any ideas for a formula? I assume proving  
the sequence is a subset of A047541 is straightforward.

Given the 4 binary blocks 100, 010, 001, 111 (or strings) and reading  
backwards ignoring leading zeros, stack (concantenated with "_",  
below) any number of these and order from least to greatest:

100 <-> 1
010 <-> 2
001 <-> 4
111 <-> 7
100_100 <-> 9
010_100 <-> 10
001_100 <-> 12
111_100 <-> 15
100_010 <-> 17
010_010 <-> 18
001_010 <-> 20
111_010 <-> 23
100_001 <-> 33
010_001 <-> 34
001_001 <-> 36
111_001 <-> 39
100_111 <-> 57
010_111 <-> 58
001_111 <-> 60
111_111 <-> 63
100_100_100 <-> 73
010_100_100 <-> 74
001_100_100 <-> 76
111_100_100 <-> 79
100_010_100 <-> 81
010_010_100 <-> 82
001_010_100 <-> 84
111_010_100 <-> 87
100_001_100 <-> 97
...

I'll wait for any replies and submit the sequence.

Sincerely,
Creigh