This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A386724 #24 Aug 14 2025 03:48:43
%S A386724 3,5,7,17,103,107,137,283,313,347,1033,2027,3257,3673,4217,4547,5023,
%T A386724 9433,9767,11833,14593,15137,15733,18253,19423,20717,20983,23537,
%U A386724 25847,26113,28753,32057,32323,33073,35053,37307,38327,39163,43607,44623,46183,46273,47743,48407
%N A386724 Twin primes p such that 6p+1, 6p-1 is a twin prime pair.
%C A386724 {3,5} and {5,7} are the only twin prime pairs occurring in this since (6p-1)*(6p+1)*(6p+11)*(6p+13) is always divisible by 5. Therefore the smallest possible gaps for p>7 is 4 (cousin primes).
%H A386724 Alois P. Heinz, <a href="/A386724/b386724.txt">Table of n, a(n) for n = 1..10000</a>
%p A386724 q:= p-> isprime(p) and ormap(isprime, [p-2, p+2]) and andmap(isprime, [6*p-1, 6*p+1]):
%p A386724 select(q, [2*i+1$i=1..25000])[]; # _Alois P. Heinz_, Jul 31 2025
%t A386724 Select[Prime[Range[5000]], Or @@ PrimeQ[# + {-2, 2}] && And @@ PrimeQ[6*# + {-1, 1}] &] (* _Amiram Eldar_, Jul 31 2025 *)
%Y A386724 Cf. A002822, A001359, A014574, A176131 (subsequence), A182481, A294731. Subset of A060212.
%K A386724 nonn
%O A386724 1,1
%A A386724 _Marc Morgenegg_, Jul 31 2025
%E A386724 More terms from _Pontus von Brömssen_, Jul 31 2025