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A006489 n-6, n, n+6 are primes.
(Formerly M4770)
14

%I M4770

%S 11,13,17,23,37,47,53,67,73,103,107,157,173,233,257,263,277,353,373,

%T 563,593,607,613,647,653,733,947,977,1097,1103,1123,1187,1223,1283,

%U 1297,1367,1433,1453,1487,1493,1607,1613,1663,1747,1753,1783,1867,1873

%N n-6, n, n+6 are primes.

%C Solutions of the equation (n-6)'+n'+(n+6)'=3, where n' is the arithmetic derivative of n. - _Paolo P. Lava_, Nov 08 2012

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A006489/b006489.txt">Table of n, a(n) for n = 1..1000</a>

%H Joseph Hirsch, <a href="http://www.jstor.org/stable/27958187">Prime Triplets</a>, Mathematics Teacher, 62 (1969), 467ff (see p. 471).

%H D. S. Kluk and N. J. A. Sloane, <a href="/A002050/a002050_3.pdf">Correspondence, 1979</a>

%t q=6*1;lst={};Do[p=Prime[n];If[PrimeQ[p-q]&&PrimeQ[p+q],AppendTo[lst,p]],{n,7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2009 *)

%t Select[Prime[Range[300]],And@@PrimeQ[#+{6,-6}]&] (* _Harvey P. Dale_, May 21 2012 *)

%o (Haskell)

%o a006489 n = a006489_list !! (n-1)

%o a006489_list = filter

%o ((== 1) . a010051 . (subtract 6)) $ dropWhile (<= 6) a023201_list

%o -- _Reinhard Zumkeller_, Feb 25 2013

%o (PARI) is(n)=isprime(n-6) && isprime(n) && isprime(n+6) \\ _Charles R Greathouse IV_, Feb 07 2017

%Y Subsequence of A023201.

%K nonn,nice,easy

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _James A. Sellers_, Dec 24 1999

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Last modified February 27 15:59 EST 2020. Contains 332307 sequences. (Running on oeis4.)