A248367 - OEIS

%I #28 Dec 17 2019 19:17:19

%S 5,71,101,191,311,821,1451,4091,4481,4931,5441,6791,12071,13721,14591,

%T 17921,18251,20441,20771,20981,21521,21611,35801,38711,41141,41981,

%U 43541,46271,47351,47741,48821,49331,53231,64151,70841

%N Initial members of prime quadruples (n, n+2, n+36, n+38).

%C This sequence is prime n, where there exist two twin prime pairs of (n,n+2), (n+36,n+38).

%C This sequence is a subsequence of A001359 (lesser of twin primes).

%C Excluding 5, this sequence is a subsequence of A132232 (primes, 11 mod 30).

%H Karl V. Keller, Jr., <a href="/A248367/b248367.txt">Table of n, a(n) for n = 1..100000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeQuadruplet.html">Prime Quadruplet.</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=71, the numbers 71, 73, 107, 109, are primes.

%t a248367[n_] := Select[Prime@Range@n, And[PrimeQ[# + 2], PrimeQ[# + 36], PrimeQ[# + 38]] &]; a248367[8000] (* _Michael De Vlieger_, Jan 11 2015 *)

%t Select[Prime[Range[8000]],AllTrue[#+{2,36,38},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Dec 17 2019 *)

%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+36) and isprime(n+38): print(n,end=', ')

%Y Cf. A077800 (twin primes), A001359, A132232, A181603 (twin primes, end 1).

%K nonn

%O 1,1

%A _Karl V. Keller, Jr._, Jan 11 2015