Are A055999 and A074171 somehow the same?

[Lßbos ElemÚr]

On 6 Oct 2004, at 10:32, Alonso Del Arte wrote:

Date sent:      	Wed, 6 Oct 2004 10:32:14 -0400
From:           	Alonso Del Arte <alonso.delarte at gmail.com>
Send reply to:  	Alonso Del Arte <alonso.delarte at gmail.com>
To:             	seqfan at ext.jussieu.fr
Subject:        	Re: Are A055999 and A074171 somehow the same?

> I think that if we can prove that A055999 and A074171 are the same
> (except for the two initial terms), then the two sequences should be
> merged, with "a(n)=n*(n+7)/2" as the primary definition; and "Start
> with 1, add the next number if one gets a prime then subtract the next
> number else add the next" as a comment.
> 
> But what holds me back from asserting this is that I don't know how to
> prove they are in fact the same. I have calculated a couple dozen more
> terms for both and they agree, but I could calculate a million terms
> and still stop short of the term that proves the two sequences are in
> fact different.
> 
> Alonso del Arte
> 
> 
> On Tue, 5 Oct 2004 14:05:08 +0200 (CEST), Michele Dondi
> <blazar at pcteor1.mi.infn.it> wrote:
> > On Tue, 5 Oct 2004, Dean Hickerson wrote:
> > 
> > > Michele Dondi asked:
> > >
> > >> Why? After all isn't OEIS supposed to be a comprehensive
> > >> encyclopedia of integer sequences?
> > >
> > > No.  Such an encyclopedia would be uncountably infinite.  The OEIS
> > > is only supposed to contain sequences which are useful or
> > > interesting.  This
> > 
> > Of course! Now incidentally this raises another question: are
> > sequences which are useful or interesting finite? Are they
> > countable?
> > 
> > > sequence is a trivial variation on a sequence that's already in
> > > the OEIS. If the sequence entry were clear and correct, then I'd
> > > be inclined to leave it in, since it was, at least momentarily, of
> > > interest to at least one person.  But the description was unclear,
> > > and would require some editor to fix it.  I think that would be a
> > > waste of the editor's time.
> > 
> > I see your point... I must admit that I hadn't read you message
> > carefully enough and I hadn't understood that the description was
> > not clear enough for OEIS.
> > 
> > Michele
> > --
> > : I'm about to learn myself perl6 (after using perl5 for some time).
> > I'm also trying to learn perl6 after using perl5 for some time.  :-)
> > - Larry Wall in perl6-language ML, 9 Jul 2004
Do not delete A074171, because its definition is dependent on 
sequence of primes...Thus the coincidence with simple polynomial
A055999 is surprizing.
I did test below n=100000. A rather speedy Mathematica program I 
 added:
-----------------------------------------------------------------------
{ta={1,3},tb={{0}}};
Do[s=Last[ta];
If[PrimeQ[s],ta=Append[ta,s-n]];
If[!PrimeQ[s],ta=Append[ta,s+n]];
Print[{a=Last[ta],b=(n-3)*(n+4)/2,a-b}];
tb=Append[tb,a-b],{n,3,100000}];{ta,{tb,Union[tb]}}
-----------------------------------------------------------------------

Regards
Labos E
labos"ana1.sote.hu