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A253627 Initial members of prime sextuples (n, n+2, n+12, n+14, n+18, n+20).

%I A253627 #16 Feb 16 2025 08:33:24
%S A253627 179,809,5639,9419,62969,88799,109829,284729,452519,626609,663569,
%T A253627 855719,983429,1003349,1146779,1322159,2116559,2144489,2668229,
%U A253627 3153569,3437699,4575269,4606559,4977419,5248079,5436269,5450099,5651729
%N A253627 Initial members of prime sextuples (n, n+2, n+12, n+14, n+18, n+20).
%C A253627 This sequence is prime n, where there exist three twin prime pairs of (n,n+2), (n+12,n+14) and (n+18,n+20).
%C A253627 This is a subsequence of each of the following: A128469(30n+29), A060229(smaller of twin primes of 30n+29).
%C A253627 The prime sextuple does not have to comprise only consecutive primes. - _Harvey P. Dale_, Aug 15 2016
%H A253627 Karl V. Keller, Jr., <a href="/A253627/b253627.txt">Table of n, a(n) for n = 1..10000</a>
%H A253627 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%H A253627 Wikipedia, <a href="http://www.wikipedia.org/wiki/Twin_prime">Twin prime</a>
%e A253627 For n= 809, the numbers, 809, 811, 821, 823, 827, 829, are primes.
%t A253627 a253627[n_] := Select[Range@n, And[PrimeQ[#], PrimeQ[# + 2], PrimeQ[# + 12], PrimeQ[# + 14], PrimeQ[# + 18], PrimeQ[# + 20]] &]; a253627[10^7] (* _Michael De Vlieger_, Jan 06 2015 *)
%t A253627 Select[Prime[Range[400000]],AllTrue[#+{2,12,14,18,20},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 15 2016 *)
%o A253627 (Python)
%o A253627 from sympy import isprime
%o A253627 for n in range(1,10000001,2):
%o A253627   if isprime(n) and isprime(n+2) and isprime(n+12) and isprime(n+14) and isprime(n+18) and isprime(n+20): print(n,end=', ')
%Y A253627 Cf. A077800 (twin primes), A001359, A128469, A060229.
%K A253627 nonn
%O A253627 1,1
%A A253627 _Karl V. Keller, Jr._, Jan 06 2015