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A190792 Primes p=prime(i) such that prime(i+3)-prime(i)=12.

%I A190792 #23 Mar 17 2023 11:04:59
%S A190792 17,19,29,31,41,59,61,67,71,127,227,229,269,271,347,431,607,641,1009,
%T A190792 1091,1277,1279,1289,1291,1427,1447,1487,1597,1601,1607,1609,1657,
%U A190792 1777,1861,1987,2129,2131,2339,2371,2377,2381,2539,2677,2687,2707,2789,2791
%N A190792 Primes p=prime(i) such that prime(i+3)-prime(i)=12.
%C A190792 Minimal distance between prime(i) and prime(i+3) is 12 if all three consecutive prime gaps are different.
%C A190792 There are 6 possible consecutive prime gap configurations:
%C A190792   {2,4,6}, {2,6,4}, {4,2,6}, {4,6,2}, {6,2,4}, and {6,4,2}.
%C A190792 Least prime quartets with such gap configurations are:
%C A190792   {17,19,23,29}->{2,4,6}
%C A190792   {29,31,37,41}->{2,6,4}
%C A190792   {67,71,73,79}->{4,2,6}
%C A190792   {19,23,29,31}->{4,6,2}
%C A190792   {1601,1607,1609,1613}->{6,2,4}
%C A190792   {31,37,41,43}->{6,4,2}.
%H A190792 Charles R Greathouse IV, <a href="/A190792/b190792.txt">Table of n, a(n) for n = 1..10000</a>
%t A190792 p = Prime[Range[1000]]; First /@ Select[Partition[p, 4, 1], Last[#] - First[#] == 12 &] (* _T. D. Noe_, May 23 2011 *)
%o A190792 (Magma) [NthPrime(i): i in [2..60000] | NthPrime(i+3)-NthPrime(i) eq 12];  // _Bruno Berselli-, May 20 2011
%o A190792 (PARI) is(n)=if(!isprime(n), return(0)); my(p=nextprime(n+1),q); if(p-n>6, return(0)); q=nextprime(p+1); q-n<11 && nextprime(q+1)-n==12 \\ _Charles R Greathouse IV_, Sep 14 2015
%Y A190792 Cf. A031165, A078847.
%K A190792 nonn,easy
%O A190792 1,1
%A A190792 _Zak Seidov_, May 20 2011