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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
2, 4, 8, 10, 14, 20, 28, 34, 38, 40, 50, 64, 68, 80, 94, 98, 104, 110, 124, 134, 154, 164, 178, 188, 190, 208, 220, 230, 238, 248, 260, 280, 308, 314, 328, 344, 370, 418, 428, 430, 440, 454, 458, 484, 518, 544, 560, 574, 584, 610, 614, 628, 638, 640, 644, 650 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

LINKS

Sameen Ahmed Khan, Table of n, a(n) for n = 1..10000

Sameen A. Khan, Primes in Geometric-Arithmetic Progression, arXiv preprint arXiv:1203.2083 [math.NT], 2012.

FORMULA

a(n) = 2 * A115334(n). - Wesley Ivan Hurt, Feb 06 2014

EXAMPLE

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

MATHEMATICA

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

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

PROG

(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

(PARI) for(n=1, 1e3, if(isprime(n + 3) && isprime(2*n + 3), print1(n, ", "))); \\ Altug Alkan, Dec 27 2015

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

CROSSREFS

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

Sequence in context: A088967 A200566 A091992 * A242247 A089033 A049422

Adjacent sequences:  A206034 A206035 A206036 * A206038 A206039 A206040

KEYWORD

nonn,easy

AUTHOR

Sameen Ahmed Khan, Feb 03 2012

STATUS

approved

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Last modified May 22 20:08 EDT 2017. Contains 286906 sequences.