A121760/1: two (interesting?) sequences

Joerg Arndt arndt at jjj.de
Tue Aug 22 01:28:37 CEST 2006


'nice' is a subjective tag.
I wouldn't have given it to, e.g.:

> 
> A068505         Value of n interpreted in base (b+1), where b=A054055(n) is the
>                 largest digit in decimal representation of n.
> 

> [...]
> 
> and 630 others.  So one asks, why are these base sequences nice and others not?
>   Typically, it is indeed because of inherent mathematical structure, or
> illumination of the base notation itself, or unexpected iterative behavior,
> though that list is not exhaustive.
> 

If some of this is the case, it should better be mentioned in a comment
(where possible at all).

If base (representation) has to be, then use
- binary if your brain is restricted to boring representations (kill decimal!)
- base -2
- 2-NAF (and, possibly w-NAF)
- rising factorial base (mixed radix)
- fibonacci representation (and similar greedy/recurrence representations)
- representations connected to combinatorial objects
- etc. whatever has a nonzero chance to be interesting


IMO: If one plays with digits and creates yet another random sequence
without connection to anything at all, no analysis at all, then the
sequence should _not_ be submitted.

Same for random expansions of random (elementary or not) functions.

When 'base' meets 'prime' all hope is lost.
When 'prime' meets addition, all hope is lost.
When 'decimal' meets about anything, all hope is lost.

When I have time I indeed look at suggested sequences mentioned on
seqfan.  However, with the sequences that started this thread I cannot
see any effort of the submitter to analyze the sequence(s).  In cases
like this I occasionally write a mail to discourage further such
submissions.  In this case (also) because the sequences are somewhat
likely to give spurious hits with searches, i.e. _lessen_ the value of
the OEIS.

just my 2 exocents






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