Are A055999 and A074171 somehow the same?

[Lßbos ElemÚr]

On 7 Oct 2004, at 8:40, Richard Guy wrote:

Date sent:      	Thu, 7 Oct 2004 08:40:26 -0600 (MDT)
From:           	Richard Guy <rkg at cpsc.ucalgary.ca>
To:             	Lßbos ElemÚr <Labos at ana.sote.hu>
Copies to:      	Alonso Del Arte <alonso.delarte at gmail.com>, seqfan at ext.jussieu.fr
Subject:        	Re: Are A055999 and A074171 somehow the same?

> Am I being very naive?  `if one gets a
> prime ...'  As  n(n+7)/2  is always
> composite, one never gets a prime.  I
> see no reason for further calculation,
> nor for the continued existence of
> A074171, except for a possible quaint
> remark at A055999, and retention for
> purely bookkeeping and historical
> reasons, with reference to A055999.  R.

> 
> On Thu, 7 Oct 2004, [ISO-8859-2] Lßbos ElemÚr wrote:
> 
> > 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

I do not know you are  naive or not. 
But anyhow.you are right. 
It is clear that prime condition never reached ...
So we see a degenerated version of an otherwise interesting 
definition. 
Nevertheless,changing initial values or introducing modest 
modifications this
family of refursions immediately becomes interesting.

Regards 
Labos

PS: In place of njas I weould keep this[=A074171] as an example of 
chess-blindness. Several people were playing around and I think not
in vain.  


Regards 
Labos