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

%I

%S 17,19,29,31,41,59,61,67,71,127,227,229,269,271,347,431,607,641,1009,

%T 1091,1277,1279,1289,1291,1427,1447,1487,1597,1601,1607,1609,1657,

%U 1777,1861,1987,2129,2131,2339,2371,2377,2381,2539,2677,2687,2707,2789,2791

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

%C Minimal distance between prime(i) and prime(i+3) is 12 if all three consecutive prime gaps are different.

%C There are 6 possible consecutive prime gap configurations:

%C {2,4,6}, {2,6,4}, {4,2,6}, {4,6,2}, {6,2,4}, and {6,4,2}.

%C Least prime quartets with such gap configurations are:

%C {17,19,23,29}->{2,4,6}

%C {29,31,37,41}->{2,6,4}

%C {67,71,73,79}->{4,2,6}

%C {19,23,29,31}->{4,6,2}

%C {1601,1607,1609,1613}->{6,2,4}

%C {31,37,41,43}->{6,4,2}.

%H Charles R Greathouse IV, <a href="/A190792/b190792.txt">Table of n, a(n) for n = 1..10000</a>

%t p = Prime[Range[1000]]; First /@ Select[Partition[p, 4, 1], Last[#] - First[#] == 12 &] (* _T. D. Noe_, May 23 2011 *)

%o (MAGMA) [NthPrime(i): i in [2..60000] | NthPrime(i+3)-NthPrime(i) eq 12]; // Bruno Berselli, May 20 2011

%o (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 Cf. A078847.

%K nonn,easy

%O 1,1

%A _Zak Seidov_, May 20 2011

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Last modified December 2 17:30 EST 2021. Contains 349445 sequences. (Running on oeis4.)