parity of integer sequences

[jeremy.gardiner at btinternet.com]

Thanks to all who responded on this subject.

I had imagined adding a new field like %P A000796 A030657 to each entry in the database, but the consensus view seems to be that enhanced search capability would be preferable to storing additional parity sequences.

I must agree, for after some experimentation with the downloaded stripped database I estimate that something like 24,000 new sequences would be generated, i.e. an additional third as many as the existing 73,000 entries.

The results from this investigation may be interesting: Having generated a parity sequence for each entry in the database I ordered these by frequency of occurrence, shown in the left hand column here for just the top part of the list.

I truncated the parity sequences to 20 terms and didn't include sequences of less than 20 terms.

4530 ,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
2691 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1900 ,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1256 ,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1167 ,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,
1074 ,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
 392 ,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
 297 ,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
 212 ,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,
 201 ,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,
 183 ,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
 175 ,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,
 174 ,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,
 168 ,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,
 162 ,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,
 161 ,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
 146 ,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,
 140 ,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,
 133 ,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,
 112 ,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,
 110 ,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,
 110 ,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,
 108 ,1,1,1,1,0,1,1,1,1,1,1,0,0,0,1,1,1,0,0,1,
  98 ,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,

Jeremy Gardiner