parity of integer sequences

[Robert G. Wilson v]

David,

        I also would like a wild card lookup capability.

Bob Wilson

David Wilson wrote:

>----- Original Message -----
>From: <jeremy.gardiner at btinternet.com>
>To: <seqfan at ext.jussieu.fr>
>Sent: Wednesday, July 31, 2002 5:36 AM
>Subject: parity of integer sequences
>
>
>>I was thinking about how to categorise integer sequences and I wonder how
>>
>useful it would be if the on-line encyclopaedia were to contain a reference
>to the parity representation for each sequence?
>
>>Many of the entries would be all odd, all even or simply alternating
>>
>parity but there are also many more interesting examples such as 1010010001
>... (A023531), however there is no easy way of data mining these without
>calculating parity for each sequence.
>
>>Of course parity is not the only way to categorise integer sequences but
>>
>it is an important property.
>
>>Perhaps other people have a view on this?
>>
>
>I agree that parity searches would be useful, however, I disagree with
>adding additional parity sequence fields to the EIS.
>
>The EIS already has two potential sets of sequence fields for each entry,
>the unsigned sequence (%STU) and the signed sequence (%VWX).  Adding
>a parity sequence would create additional fields, bloating the database
>further.
>The logical extreme, adding a new set of fields to each EIS entry for each
>search criterion, is clearly silly.
>
>I would incline in the other direction, that of decreasing the bulk of the
>EIS
>database and increasing its search capabilities.  Optimally, each EIS entry
>would contain only the signed sequence.  The search criteria would consist
>of a lookup sequence and a transform function.
>
>The lookup sequence would be an extended version of the current lookup
>sequence. I would recommend adding
>
>   ? to match a single unknown element
>   * to match zero or more unknown elements
>   + to match one or more unknown elments
>   ^ to match the beginning of sequence
>
>Thus
>
>   13,125 matches sequences containing adjacent elements 13,125
>   ^13,125 matches sequences starting with 13,125
>   13,?,125 matches sequences containing 13 followed by 125 with one
>intervening element.
>   13,*,125 matches sequence in which 13 occurs prior to 125.
>
>The transform function is a function in the variable "n" applied prior to
>matching the lookup.
>Thus, if the transform function were "n mod 2", and the lookup sequence were
>0,1,1,0,0,1,1,0,0,1,1,0 we might would match the triangular numbers.  I
>leave the
>expression syntax undefined, but MMa expressions (for their math
>capabilities) and
>Perl expressions (for their pattern matching capabilities) spring to mind.
>
>This mechanism would provide fairly flexible search capabilities.  We could
>use %STU
>to store the signed sequence, eliminate %VWX, and use "abs(n)" function to
>search the
>unsigned sequences.  I would recommend generating indexes for searches on
>various
>common transform functions such as "n", "abs(n)", "n mod 2", etc.  Searches
>on less
>common transform functions would necessarily be slower, but possible.
>
>

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