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<P><TT>OK, since I get a rave review, here's my full-blown proposal for</TT>
<BR><TT>generalized indexing of Sloane sequences:</TT>
<BR><TT> </TT>
<BR><TT>Redefine the %O line to support a simple index sequence description</TT>
<BR><TT>language:</TT>
<BR><TT> </TT>
<BR><TT><oline> := "%O" <anum> <int> ";" <mdidx>
// %O line</TT>
<BR><TT><mdidx> := <idx> ( "X" <idx> )*
// Multi-dimensional index</TT>
<BR><TT><idx> := <idx> ( "," <idx> )*
// Concatenated index</TT>
<BR><TT><idx> := <int> to <xint> by <int>
// Integer-spaced interval index</TT>
<BR><TT><idx> := <int> to <xint>
// Unit-spaced interval index</TT>
<BR><TT><idx> := <int>
// Integer index</TT>
<BR><TT><idx> := <anum>
// Sloane sequence index</TT>
<BR><TT><xint> := <int> | "inf" | "-inf" | "?"
// Extended integer</TT>
<BR><TT><int> := integer constant
// Integer</TT>
<BR><TT><anum> := Sloane A-number
// Sloane sequence A-number</TT>
<BR><TT> </TT>
<BR><TT>Thus we have:</TT>
<BR><TT> </TT>
<BR><TT>%O A000040 1; 1 to inf
// 1, 2, 3, 4, ...</TT>
<BR><TT>%O A000367 6; 0 to inf by 2
// 0, 2, 4, 6, ...</TT>
<BR><TT>%O A001918 2; A000040
// 2, 3, 5, 7, 11, ...</TT>
<BR><TT>%O A002181 2; A002202
// 1, 2, 4, 6, 8, ...</TT>
<BR><TT>%O A007318 5; A003056 X A002262
// (0,0), (1,0), (1,1), ...</TT>
<BR><TT> </TT>
<BR><TT>In the new %O line, the first number is the same as the second
number</TT>
<BR><TT>of the current %O line, that is, the raw index of the first nontrivial</TT>
<BR><TT>element (or 0 if no such element exists). The expression
after the</TT>
<BR><TT>semicolon describes the index sequence. The free-form indexing
allows</TT>
<BR><TT>us to deal with multi-dimensional integer functions, nonstandard</TT>
<BR><TT>indexing, unknown elements, etc.</TT>
<BR><TT> </TT>
<BR><TT>The simplest index sequences (finite sets or ranges, natural numbers,</TT>
<BR><TT>even numbers, etc) can be described in a straightforward fasion
(e.g,</TT>
<BR><TT>"1 to inf" as opposed to "A000027"). Describing the index
sequence on</TT>
<BR><TT>the %O line allows programs to easily obtain the index sequence
(harder</TT>
<BR><TT>if index information is buried in a comment on a %C line).</TT>
<BR><TT> </TT>
<BR><TT>In most cases, the existing %O format can be automatically converted
to</TT>
<BR><TT>the new %O format without changing the meaning at all. For
instance,</TT>
<BR><TT>with an infinite sequence it suffices to change "%O A002859 x,y"
to</TT>
<BR><TT>"%O A002859 y; x to inf", and the fix for finite full sequences
is</TT>
<BR><TT>equally trivial. Only non-full finite sequences need be considered</TT>
<BR><TT>case-by-case.</TT>
<BR><TT> </TT>
<BR><TT>After conversion, we have a means to specify indexing for tabular
and</TT>
<BR><TT>nonstandard sequences. This doesn't have to be done at one
shot for</TT>
<BR><TT>50,000 sequences, but can be improved over time like other information</TT>
<BR><TT>in the database.</TT>
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