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A206037 Values of the difference d for 3 primes in arithmetic progression with the minimal start sequence {3 + j*d}, j = 0 to 2. 11

%I

%S 2,4,8,10,14,20,28,34,38,40,50,64,68,80,94,98,104,110,124,134,154,164,

%T 178,188,190,208,220,230,238,248,260,280,308,314,328,344,370,418,428,

%U 430,440,454,458,484,518,544,560,574,584,610,614,628,638,640,644,650

%N Values of the difference d for 3 primes in arithmetic progression with the minimal start sequence {3 + j*d}, j = 0 to 2.

%C The computations were done without any assumptions on the form of d.

%C Numbers n such that n+3 and 2n+3 are both primes.

%H Sameen Ahmed Khan, <a href="/A206037/b206037.txt">Table of n, a(n) for n = 1..10000</a>

%H Sameen A. Khan, <a href="http://arxiv.org/abs/1203.2083">Primes in Geometric-Arithmetic Progression</a>, arXiv preprint arXiv:1203.2083 [math.NT], 2012.

%F a(n) = 2 * A115334(n). - _Wesley Ivan Hurt_, Feb 06 2014

%e d = 8 then {3, 3 + 1*8, 3 + 2*8} = {3, 11, 19}, which is 3 primes in arithmetic progression.

%t t={}; Do[If[PrimeQ[{3, 3 + d, 3 + 2*d}] == {True, True, True}, AppendTo[t, d]], {d, 1000}]; t

%t Select[Range[2,700,2],And@@PrimeQ[{3+#,3+2#}]&] (* _Harvey P. Dale_, Sep 25 2013 *)

%o (TI-Basic) Clrio:Input "n",n:Lbl colorin:If isPrime(n+3) and isPrime(2*n+3) Then:Disp n:Pause:Endif:n+1(sto)n:Goto colorin:EndPrgm " _César Aguilera_, Dec 27 2015

%o (PARI) for(n=1, 1e3, if(isprime(n + 3) && isprime(2*n + 3), print1(n, ", "))); \\ _Altug Alkan_, Dec 27 2015

%o (MAGMA) [n: n in [1..700] | IsPrime(3+n) and IsPrime(3+2*n)]; // _Vincenzo Librandi_, Dec 28 2015

%Y Cf. A040976, A206038, A206039, A206040, A206041, A206042, A206043, A206044, A206045.

%K nonn,easy

%O 1,1

%A _Sameen Ahmed Khan_, Feb 03 2012

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Last modified July 8 03:38 EDT 2020. Contains 335504 sequences. (Running on oeis4.)