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%I #34 Mar 13 2023 10:19:00
%S 47,151,167,251,257,367,557,587,601,647,727,941,971,1097,1117,1181,
%T 1217,1361,1741,1747,1901,2281,2411,2671,2897,2957,3301,3307,3631,
%U 3727,4007,4451,4591,4651,4987,5101,5107,5297,5381,5387,5557,5801,6067,6257,6311
%N Smallest of three consecutive primes with a difference of 6: primes p such that p+6 and p+12 are the next two primes.
%C Subsequence of A031924.
%H T. D. Noe, <a href="/A047948/b047948.txt">Table of n, a(n) for n=1..1000</a>
%F Let p(k) be the k-th prime; sequence gives p(n) such that p(n+2)-p(n+1)=p(n+1)-p(n)=6.
%e 47 is a term as the next two primes are 53 and 59.
%t ok[p_] := (q = NextPrime[p]) == p+6 && NextPrime[q] == q+6; Select[Prime /@ Range[1000], ok][[;; 45]] (* _Jean-François Alcover_, Jul 11 2011 *)
%t Transpose[Select[Partition[Prime[Range[1000]],3,1],Differences[#]=={6,6}&]] [[1]] (* _Harvey P. Dale_, Apr 25 2014 *)
%o (PARI) is_A047948(n)={nextprime(n+1)==n+6 && nextprime(n+7)==n+12 && isprime(n)} \\ _Charles R Greathouse IV_, Aug 17 2011, simplified by _M. F. Hasler_, Jan 13 2013
%o (PARI) p=2;q=3;forprime(r=5,1e4,if(r-p==12&&q-p==6,print1(p", "));p=q;q=r) \\ _Charles R Greathouse IV_, Aug 17 2011
%Y Cf. A031924, A078853, A046789.
%Y Cf. A033451 (four consecutive primes with difference 6)
%Y Cf. A001223, A033451, A052197, A052198.
%K easy,nonn
%O 1,1
%A _Enoch Haga_
%E Corrected by _T. D. Noe_, Mar 07 2008
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