A138479: no soln for n=13

[zak seidov]

Case 13 has no solution because
26+p^2 is divisible by 3, for any prime p>3,
zak

--- Artur <grafix at csl.pl> wrote:

> a = {}; Do[p = 0; While[(! PrimeQ[2*n + Prime[p +
> 1]^2]) && (p < 10), 
> p++]; If[p < 10, AppendTo[a, Prime[p + 1]],
> AppendTo[a, 0]], {n, 1, 
> 150}]; a (*Artur Jasinski*)
> 
> 3, 3, 5, 3, 3, 5, 3, 5, 5, 3, 3, 7, 0, 3, 7, 3, 3,
> 5, 3, 7, 5, 3, 5, 5, 
> 3, 3,
> 5, 0, 3, 7, 3, 3, 29, 0, 3, 5, 3, 5, 5, 3, 5, 5, 0,
> 3, 7, 3, 3, 19, 3, 
> 3, 5,
> 3, 5, 7, 0, 5, 5, 0, 3, 11, 3, 5, 5, 3, 3, 5, 0, 11,
> 5, 3, 3, 7, 0, 3, 
> 7, 0,
> 3, 5, 3, 11, 7, 3, 5, 5, 3, 3, 5, 0, 7, 7, 3, 3, 5,
> 3, 3, 7, 0, 11, 5, 
> 0, 3,
> 5, 0, 5, 11, 0, 3, 5, 3, 3, 7, 3, 5, 7, 3, 3, 7, 0,
> 5, 13, 3, 5, 5, 3, 
> 13, 5,
> 3, 5, 5, 3, 3, 7, 0, 3, 13, 3, 3, 11, 0, 11, 5, 3,
> 5, 5, 0, 5, 13, 0, 3, 7
> 
> 
> Lallouet pisze:
> > To attention of Robert G Wilson v.
> >  
> > Dear Robert
> >  
> > I send you this message through seqfans as those
> sent directly to your 
> > address rgwv at rgwv.com <mailto:rgwv at rgwv.com> are
> systematically 
> > returned undelivered, I don't know why.
> >  
> > I thank you to have taken some of your time to
> look to my sequence 
> > A138479 
> >  
> > But I am astonished of your reaction to its
> publication.
> >
> > Indeed after verifications , I don't find any
> error.
> >
> > 11=2+3^2      hence a(1) =3
> > 13=4 +3^2     hence a(2)=3
> > 31=6+5^2      hence a(3)=5
> > 17=8+3^2      hence a(4)=3
> > 19=10+3^2    hence a(5)=3
> > 37=12+5^2    hence  a(6)=5
> > 23=14+3^2    hence a(7)=3
> > 41=16+5^2    hence a(8)=5
> > 43=18+5^2    henec a(9)=5
> > 29=20+3^2    hence a(10)=3
> > 31=22+3^2    hence a(11)=3
> > 73=24+7^2    hence a(12)=7
> > I did'nt  find any solution for n=13 for any
> 2*n+p^2 less than 10^6, 
> > which
> > explains my conjecture.
> > I think you have not paid attention to the
> difference between the 
> > definitions of the two sequences.For my sequence 
> 2*n
> > =difference between a prime and a SQUARE of
> another prime) and for 
> > A0204483 , 2*n=difference between two primes)
> > As I was not sure of the interest of my sequence,
> I first consulted 
> > Seqfans
> > and I received a reply from Richar MATHAR, who
> pointed the similitude but
> > not identity with other already published
> sequences, which encouraged 
> > me to
> > submit it to EOIS, but in another form. You will
> find these two messages
> > here joined, with also my complete definitive
> submission.
> > As you can see my  publication has been controlled
> , I don't know by 
> > whom,and partly cut. 
> > It has not been changed for the 12th first
> published terms. But  my 
> > conjecture  has
> > been reduced only to the first value of the index 
> (13) for which no
> > solution had been found. and  the possible band
> between all the 
> > greater voids in  my
> > sequence (13,28,34,43,55,58,67,73,76,88,97, , , ,
> , ) and the sequence
> > A059324 has disappeared . It was only a conjecture
> that my level in
> > mathematics is not sufficient to prove , but I
> thought that this problem
> > was the most interesting part in my publication
> and one of the reasons 
> > of my call
> > for help to seqfans.
> > Anyway if senior mathematicians think differently,
> I am too old to die if
> > the sequence is eliminated.
> > I should be happy however to read your eventual
> comments after having 
> > read
> > these precisions.
> > Best regards
> > Philippe LALLOUET
> >  
> > A copy has been sent to Neil Sloane and has not
> been returned.
> >
> >
> >
> >
> > ----- Original Message -----
> > From: "Robert G. Wilson v" <rgwv at rgwv.com>
> > To: "Neil J. A. Sloane" <njas at research.att.com>;
> "Philippe Lallouet"
> > <philip.lallouet at orange.fr>; "Philippe Lallouet"
> > <philip.lallouet at wanadoo.fr>
> > Sent: Wednesday, March 26, 2008 4:54 AM
> > Subject: DELETE A138479.
> >
> >
> > > Neil,
> > >
> > >    Once the sequence is corrected for errors
> then the sequence below is
> > > A020483
> > > and therefore this sequence should be
> eliminated.
> > >
> > > Thanx, Bob.
> > >
> > >
> > > %I A138479
> > > %S A138479 3,3,5,3,3,5,3,5,5,3,3,7
> > > %N A138479 a(n) = smallest prime p such that
> 2*n+p^2 is another 
> > prime, or
> > > 0 if no such prime exists.
> > > %C A138479 I conjecture that a(13) = 0, or in
> other words, among the
> > > infinity of prime numbers, there is no pair
> (p,q>p^2) such that q-p^2 =
> > > 26.
> > > %e A138479 2+3^2=11 = prime, hence a(1) =3
> > > %e A138479 4+3^2=13 = preme, hence a(2) =3
> > > %Y A138479 Cf. A002373, A020481, A049613,
> A059324 (?).
> > > %K A138479 nonn,more,hard,new
> > > %O A138479 1,1
> > > %A A138479 Philippe LALLOUET
> (philip.lallouet(AT)orange.fr), Mar 20 2008
> > >
> >
> >
> > __________ NOD32 Informacje 2701 (20071204)
> __________
> >
> > Wiadomosc zostala sprawdzona przez System
> Antywirusowy NOD32
> > http://www.nod32.com lub http://www.nod32.pl
> 



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