A138479

[Artur]

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