A248661 - OEIS

%I #15 Nov 11 2024 21:19:34

%S 5,17,137,227,827,1427,1667,1877,2027,2087,2657,3527,3767,4217,4967,

%T 10037,11117,11777,12107,13877,17987,19697,20717,21557,22037,23687,

%U 24977,27527,27737,34157,37307,41177,42017,42407,47657,48677

%N Initial members of prime quadruples (n, n+2, n+54, n+56).

%C This sequence is prime n, where there exist two twin prime pairs of (n,n+2), (n+54,n+56).

%C Excluding 5, this is a subsequence of each of the following: A128468 (a(n)=30*n+17), A039949 (primes, 30n-13), A181605 (twin primes, end 7), and A092340 (prime n, where n^2+2*n divides (fibonacci(n^2)+fibonacci(2*n))).

%H Karl V. Keller, Jr., <a href="/A248661/b248661.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=17, the numbers 17, 19, 71, 73, are primes.

%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+54) and isprime(n+56): print(n,end=', ')

%Y Cf. A077800 (twin primes), A128468, A039949, A181605, A092340.

%K nonn

%O 1,1

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