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 A384298 #16 May 30 2025 10:39:53
%S A384298 7,67,97,487,757,1567,1597,2377,3907,7687,8677,12097,12907,13147,
%T A384298 14407,14767,15667,16057,19417,21487,31177,38317,43777,52567,57637,
%U A384298 58897,65167,65827,67477,67927,74857,81547,90007,90187,93967,94777,95467,95617,102547,111427,112237,114757,123817,129277
%N A384298 Primes p such that p + 4, p + 12 and p + 16 are also primes.
%C A384298 Initial members of prime quartets that correspond to the difference pattern [4, 8, 4].
%H A384298 Michael De Vlieger, <a href="/A384298/b384298.txt">Table of n, a(n) for n = 1..10000</a>
%F A384298 a(n) == 7 (mod 30).
%e A384298 p=97: 97+4=101, 97+12=109, 97+16=113 —> prime quartet: (97, 101, 109, 113).
%p A384298 q:= n-> andmap(i-> isprime(n+4*i), [0,1,3,4]):
%p A384298 select(q, [7+30*i$i=0..4309])[]; # _Alois P. Heinz_, May 29 2025
%t A384298 Select[Prime[Range[12099]],AllTrue[#+{4,12,16},PrimeQ]&] (* _James C. McMahon_, May 29 2025 *)
%Y A384298 Cf. A000040, A001223.
%Y A384298 Cf. A136162 [2, 4, 2], A052378 [4, 2, 4], A382810 [6, 4, 6].
%K A384298 nonn
%O A384298 1,1
%A A384298 _Alexander Yutkin_, May 25 2025