I was do mistake(too small p limit) in previos Mathematica code good
should be
a = {}; Do[p = 0; While[(! PrimeQ[2*n + Prime[p + 1]2]) && (p < 1000),
p++]; If[p < 1000, AppendTo[a, Prime[p + 1]], AppendTo[a, 0]], {n, 1,
150}]; a (*Artur Jasinski*)
And now A138479 will be
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
New sequence related with A138479 is:
A000001 Hypothetical numbers k such that no existed primes of the form
2*k + p^2 for anyone prime p
13, 28, 34, 43, 55, 58, 67, 73, 76, 88, 97, 100, 103, 106, 118, 133, 139,
145, 148, 157, 160, 163, 166, 178, 181, 184, 193, 199, 202, 208, 214, 223,
232, 238, 244, 253, 259, 262, 265, 268, 271, 283, 286, 298, 301, 307, 310,
313, 328, 331, 340, 343, 349, 352, 358, 361, 364, 370, 373, 379, 385, 388,
391, 397, 403, 412, 418, 421, 430, 433, 442, 445, 448, 454, 457, 463, 475,
478, 490, 493, 496, 499, 508, 514, 517, 523, 529, 532, 535, 538
a = {}; Do[p = 0; While[(! PrimeQ[2*n + Prime[p + 1]^2]) && (p < 1000),
p++]; If[p < 1000, , AppendTo[a, n]], {n, 1, 550}]; a
BEST WISHES
ARTUR
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
> >
>
>
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