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A078946 Primes p such that p, p+2, p+6, p+12 and p+14 are consecutive primes.

%I A078946 #43 Feb 21 2025 06:14:37
%S A078946 17,227,1277,1607,3527,3917,4637,4787,27737,38447,39227,44267,71327,
%T A078946 97367,99707,113147,122027,122387,124337,165707,183497,187127,191447,
%U A078946 197957,198827,275447,290657,312197,317957,347057,349397,416387,418337,421697,427067,443867
%N A078946 Primes p such that p, p+2, p+6, p+12 and p+14 are consecutive primes.
%H A078946 Amiram Eldar, <a href="/A078946/b078946.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%H A078946 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeTriplet.html">Prime Triplet</a>.
%F A078946 a(n) == 17 (mod 30). - _Amiram Eldar_, Feb 21 2025
%e A078946 227 is in the sequence since 227, 229 = 227 + 2, 233 = 227 + 6, 239 = 227 + 12 and 241 = 227 + 14 are consecutive primes.
%t A078946 Rest@ Select[Prime@ Range@ 36000, AllTrue[{2, 6, 12, 14} + #, PrimeQ] &] (* _Michael De Vlieger_, Apr 18 2015, Version 10 *)
%t A078946 Select[Partition[Prime[Range[36000]],5,1],Differences[#]=={2,4,6,2}&][[All,1]] (* _Harvey P. Dale_, Jun 14 2022 *)
%o A078946 (PARI) isok(p) = isprime(p) && (nextprime(p+1)==p+2) && (nextprime(p+3)== p+6) && (nextprime(p+7)==p+12) && (nextprime(p+13)==p+14); \\ _Michel Marcus_, Dec 10 2013
%o A078946 (PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 2 && p3 - p2 == 4 && p4 - p3 == 6 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ _Amiram Eldar_, Feb 21 2025
%o A078946 (Magma) [p: p in PrimesInInterval(7,1000000) | forall{i: i in [2,6,12,14] | IsPrime(p+i)}]; // _Vincenzo Librandi_, Apr 19 2015
%Y A078946 Subsequence of A128468.
%Y A078946 Subsequence of A078847. - _R. J. Mathar_, Feb 10 2013
%Y A078946 Cf. A001223, A078866, A078867, A078947-A078971, A022006, A022007.
%K A078946 nonn
%O A078946 1,1
%A A078946 _Labos Elemer_, Dec 19 2002
%E A078946 Edited by _Dean Hickerson_, Dec 20 2002