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A271000 Table read by rows: list of prime sextuplets (p, p+4, p+6, p+10, p+12, p+16).

%I A271000 #33 Feb 16 2025 08:33:32
%S A271000 7,11,13,17,19,23,97,101,103,107,109,113,16057,16061,16063,16067,
%T A271000 16069,16073,19417,19421,19423,19427,19429,19433,43777,43781,43783,
%U A271000 43787,43789,43793,1091257,1091261,1091263,1091267,1091269,1091273,1615837,1615841,1615843,1615847,1615849,1615853
%N A271000 Table read by rows: list of prime sextuplets (p, p+4, p+6, p+10, p+12, p+16).
%C A271000 A prime sextuplet is a constellation of six successive primes with distance 16, and is of the form (p, p+4, p+6, p+10, p+12, p+16).
%C A271000 Initial members p (other than 7) of prime sextuplets are congruent to 97 (mod 210). - _Ash, David_, Aug 04 2017
%H A271000 Arkadiusz Wesolowski, <a href="/A271000/b271000.txt">Table of n, a(n) for n = 1..5940</a>
%H A271000 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/1685.html">Prime Curios!: 6763998516837</a>
%H A271000 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeConstellation.html">Prime Constellation</a>
%H A271000 Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_quadruplet">Prime quadruplet</a>
%H A271000 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%F A271000 a(6*n-5) = A022008(n).
%t A271000 m = {0, 4, 6, 10, 12, 16}; Union@ Flatten@ Map[# + m &, Select[Prime@ Range[2*10^5], Times @@ Boole@ PrimeQ[# + m] == 1 &]] (* _Michael De Vlieger_, Jul 13 2016 *)
%o A271000 (Magma) lst:=[]; for p in [5..1615837 by 2] do if p le 7 xor p mod 210 eq 97 then if IsPrime(p) then t:=[c: c in [p+4..p+16] | IsPrime(c)]; if #t eq 5 then lst:=lst cat [p] cat t; end if; end if; end if; end for; lst;
%Y A271000 Cf. A022008, A270999.
%K A271000 nonn,tabf
%O A271000 1,1
%A A271000 _Arkadiusz Wesolowski_, Jul 12 2016