Heavily referenced sequences

[franktaw at netscape.net]

From: Marc LeBrun mlb at fxpt.com

>> 7. A007088 (293 references) Numbers written in base 2. 
>> I would vote no on this one. Should it have the base keyword? 
> 
>I agree with "no", and that it should have the base keyword. 
> 
>It might be nice if a comment was added mentioning that this 
>sequence is 2[n]10 in the "rebase" notation explained in other 
>entires in the OEIS. 

The primary reason one might not add the base keyword is that this can also be described as "numbers that can be expressed as sums of distinct powers of 10."
 
There is a table for this for different bases, A104257, which does not have the base keyword.  The sequence for base 2 (A000027), of course does not.  Bases 3 (A005836), 4 (A000695), and 10 (A007088) also do not, but bases 5 to 9 (A033042 to A033046) and 11 to 16 (A033047 to A033052) do.


>> 8. A006530 (292 references) Largest prime dividing n (with a(1) = 1). 
>> Probably not. 
>> 25. A020639 (175 references) Lpf(n): least prime dividing n (a(1)=1). 
>> No. 
> 
>I'd tend to consider these fairly fundamental. But then it's not clear 
>what "core" means anyway (although it's at least not as confused as "base"!) 
 
They are borderline, in my estimation.  I wouldn't object if they were made core.
 
>> 12. A000796(239 references) Decimal expansion of Pi. 
>> I'm inclined to think that this and A001113 (Decimal expansion of e) should be core sequences. 
> 
>I don't find the random encryption of interesting numbers into decimal and their subsequent 
>explosion into a sequence of digits in any sense "core", but...your tastes may differ. 
> 
>However these should certainly have the "base" keyword added. 

 
In general, decimal (or other base) expansions of real numbers have the "cons" keyword; they then do not have the "base" keyword.
 
>BTW, the search "decimal" -keyword:base currently returns 4403 hits, with "binary" it's 2637. 

 
By no means all of those should have the "base" keyword.
 
I'm currently in the process of surveying to try to find all the sequences I think should have the "base" keyword that don't.  The operational definition I'm using is "sequences that treat numbers as numerals in some part of their definition, excluding expansions of real constants".  Any more limiting definition would require that the sequences that now have the keyword be surveyed as well, to determine which ones should not have it.

>Another suggestion: it would be good if all the superseeker transforms of all the "core" 
>sequences could be generated and any missing ones added to the OEIS. That is, the OEIS would 
>contain the entire "distance-1 superseeker neighborhood" of the core group. 

 
An interesting suggestion.

 
>It would furthermore be interesting to know which sequences were the transforms of more than 
>one core sequence, even more so if they are currently missing. 
 
Franklin T. Adams-Watters
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