Are A055999 and A074171 somehow the same?

[Richard Guy]

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
>