|
%I #17 Jan 16 2015 19:21:09
%S 11,29,41,71,107,149,197,239,281,431,569,827,1019,1031,1061,1289,1451,
%T 1667,1997,2081,2111,2237,2309,2657,2969,3299,3329,3359,3527,3821,
%U 4019,4127,4229,4241,4517,5849,6269,6659,6761,7457,7559,8597
%N Initial members of prime quadruples (n, n+2, n+30, n+32).
%C This sequence is prime n, where there exist two twin prime pairs of (n, n+2, n+30, n+32).
%C This sequence is a subsequence of A001359 (lesser of twin primes).
%C The subset of terms ending in 1 in this sequence is a subsequence of A132232 (primes, 11 mod 30).
%C The subset of terms ending in 7 in this sequence is a subsequence of A141860 (primes, 2 mod 15).
%C The subset of terms ending in 9 in this sequence is a subsequence of A132236 (primes, 29 mod 30).
%H Karl V. Keller, Jr., <a href="/A247089/b247089.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=11, the numbers 11, 13, 41, 43, are primes.
%t a247089[n_] := Select[Prime@ Range@ n, And[PrimeQ[# + 2], PrimeQ[# + 30], PrimeQ[# + 32]] &]; a247089[1100] (* _Michael De Vlieger_, Jan 11 2015 *)
%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+30) and isprime(n+32): print(n,end=', ')
%Y Cf. A077800 (twin primes), A001359, A132232, A132236, A141860, A181603 (twins, end 1), A181605 (twins, end 7), A181606 (twins, end 9).
%K nonn
%O 1,1
%A _Karl V. Keller, Jr._, Jan 10 2015
|
