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Initial members of prime sextuples (n, n+2, n+12, n+14, n+18, n+20).
1

%I #15 Nov 06 2024 15:27:13

%S 179,809,5639,9419,62969,88799,109829,284729,452519,626609,663569,

%T 855719,983429,1003349,1146779,1322159,2116559,2144489,2668229,

%U 3153569,3437699,4575269,4606559,4977419,5248079,5436269,5450099,5651729

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

%C 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 This is a subsequence of each of the following: A128469(30n+29), A060229(smaller of twin primes of 30n+29).

%C The prime sextuple does not have to comprise only consecutive primes. - _Harvey P. Dale_, Aug 15 2016

%H Karl V. Keller, Jr., <a href="/A253627/b253627.txt">Table of n, a(n) for n = 1..10000</a>

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

%H Wikipedia, <a href="http://www.wikipedia.org/wiki/Twin_prime">Twin prime</a>

%e For n= 809, the numbers, 809, 811, 821, 823, 827, 829, are primes.

%t 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 Select[Prime[Range[400000]],AllTrue[#+{2,12,14,18,20},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 15 2016 *)

%o (Python)

%o from sympy import isprime

%o for n in range(1,10000001,2):

%o 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 Cf. A077800 (twin primes), A001359, A128469, A060229.

%K nonn

%O 1,1

%A _Karl V. Keller, Jr._, Jan 06 2015