cp's OEIS Frontend

A270998 Table read by rows: list of prime 5-tuples of the form (p, p+2, p+6, p+8, p+12).

%I A270998 #33 Feb 16 2025 08:33:32
%S A270998 5,7,11,13,17,11,13,17,19,23,101,103,107,109,113,1481,1483,1487,1489,
%T A270998 1493,16061,16063,16067,16069,16073,19421,19423,19427,19429,19433,
%U A270998 21011,21013,21017,21019,21023,22271,22273,22277,22279,22283,43781,43783,43787,43789,43793
%N A270998 Table read by rows: list of prime 5-tuples of the form (p, p+2, p+6, p+8, p+12).
%C A270998 A prime 5-tuple is a constellation of five successive primes with distance 12, and is of the form (p, p+2, p+6, p+8, p+12) or (p, p+4, p+6, p+10, p+12).
%C A270998 Initial members p (other than 5) of prime 5-tuples of the form (p, p+2, p+6, p+8, p+12) are congruent to 11 or 101 (mod 210).
%C A270998 Also called prime 5-tuples of the first kind.
%H A270998 Harvey P. Dale, <a href="/A270998/b270998.txt">Table of n, a(n) for n = 1..1000</a>
%H A270998 C. K. Caldwell, Top Twenty page, <a href="https://t5k.org/top20/page.php?id=56">Quintuplet</a>
%H A270998 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeConstellation.html">Prime Constellation</a>
%H A270998 Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_quadruplet">Prime quadruplet</a>
%H A270998 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%F A270998 a(5*n-4) = A022006(n).
%t A270998 m = {0, 2, 6, 8, 12}; Union@ Flatten@ Map[# + m &, Select[Prime@ Range[10^4], Times @@ Boole@ PrimeQ[# + m] == 1 &]] (* _Michael De Vlieger_, Jul 13 2016 *)
%t A270998 Select[Partition[Prime[Range[5000]],5,1],Differences[#]=={2,4,2,4}&]// Flatten (* _Harvey P. Dale_, Jul 27 2020 *)
%o A270998 (Magma) lst:=[]; for p in [5..43781 by 2] do if p eq 5 xor p mod 210 in {11, 101} then if IsPrime(p) then t:=[c: c in [p+2..p+12] | IsPrime(c)]; if #t eq 4 then lst:=lst cat [p] cat t; end if; end if; end if; end for; lst;
%Y A270998 Cf. A022006, A270999.
%K A270998 nonn,tabf
%O A270998 1,1
%A A270998 _Arkadiusz Wesolowski_, Jul 12 2016