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A252862 Initial members of prime sextuples (n, n+2, n+6, n+8, n+18, n+20).

%I A252862 #20 May 22 2025 10:21:41
%S A252862 11,18041,97841,165701,392261,663581,1002341,1068701,1155611,1329701,
%T A252862 1592861,1678751,1718861,1748471,2159231,2168651,2177501,2458661,
%U A252862 2596661,3215741,3295541,3416051,3919241,4353311,5168921,5201291,5205461,6404771
%N A252862 Initial members of prime sextuples (n, n+2, n+6, n+8, n+18, n+20).
%C A252862 This sequence is prime n, where there exist three twin prime pairs of (n,n+2), (n+6,n+8) and (n+18,n+20).
%C A252862 This is a subsequence of A132232 (Primes congruent to 11 mod 30 ).
%C A252862 Also, this is a subsequence of A128467 (30k+11).
%H A252862 Karl V. Keller, Jr., <a href="/A252862/b252862.txt">Table of n, a(n) for n = 1..10000</a>
%H A252862 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%H A252862 Wikipedia, <a href="http://www.wikipedia.org/wiki/Twin_prime">Twin prime</a>
%e A252862 For n = 18041, the numbers, 18041, 18043, 18047, 18049, 18059, 18061, are primes.
%t A252862 Select[Prime[Range[2500]], Union[PrimeQ[{#, # + 2, # + 6, # + 8, # + 18, # + 20}]] = {True} &] (* _Alonso del Arte_, Dec 23 2014 *)
%t A252862 Select[Prime[Range[450000]],AllTrue[#+{2,6,8,18,20},PrimeQ]&] (* _Harvey P. Dale_, Jun 11 2023 *)
%o A252862 (Python)
%o A252862 from sympy import isprime
%o A252862 for n in range(1,10000001,2):
%o A252862   if isprime(n) and isprime(n+2) and isprime(n+6) and isprime(n+8) and isprime(n+18) and isprime(n+20): print(n,end=', ')
%o A252862 (PARI) forprime(p=1,10^7,if(isprime(p+2) && isprime(p+6) && isprime(p+8) && isprime(p+18) && isprime(p+20), print1(p,", "))) \\ _Derek Orr_, Dec 31 2014
%Y A252862 Cf. A077800 (twin primes), A030430 (primes,10*n+1), A132232, A128467, A172456.
%K A252862 nonn
%O A252862 1,1
%A A252862 _Karl V. Keller, Jr._, Dec 23 2014