A270998 - OEIS

%I #32 Apr 03 2023 10:36:13

%S 5,7,11,13,17,11,13,17,19,23,101,103,107,109,113,1481,1483,1487,1489,

%T 1493,16061,16063,16067,16069,16073,19421,19423,19427,19429,19433,

%U 21011,21013,21017,21019,21023,22271,22273,22277,22279,22283,43781,43783,43787,43789,43793

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

%C 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 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 Also called prime 5-tuples of the first kind.

%H Harvey P. Dale, <a href="/A270998/b270998.txt">Table of n, a(n) for n = 1..1000</a>

%H C. K. Caldwell, Top Twenty page, <a href="https://t5k.org/top20/page.php?id=56">Quintuplet</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeConstellation.html">Prime Constellation</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_quadruplet">Prime quadruplet</a>

%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>

%F a(5*n-4) = A022006(n).

%t 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 Select[Partition[Prime[Range[5000]],5,1],Differences[#]=={2,4,2,4}&]// Flatten (* _Harvey P. Dale_, Jul 27 2020 *)

%o (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 Cf. A022006, A270999.

%K nonn,tabf

%O 1,1

%A _Arkadiusz Wesolowski_, Jul 12 2016