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 A377318 #23 Jun 17 2025 18:04:37
%S A377318 3,5,13,18,54,110,116,182,234,252,271,284,351,387,464,541,551,682,709,
%T A377318 717,741,821,829,1171,1417,1448,1510,1594,1711,1726,1842,1853,2009,
%U A377318 2086,2209,2297,2408,2600,2680,2876,2924,2930,3253,3303,3437,3977,4384,4431
%N A377318 Numbers k such that prime(k), prime(k)+6, prime(k)+12, and prime(k)+18 are primes.
%H A377318 Harvey P. Dale, <a href="/A377318/b377318.txt">Table of n, a(n) for n = 1..1000</a>
%F A377318 a(n) = pi(A023271(n)).
%e A377318 5 is in this sequence because: prime(5) = 11 and 11+6=17, 11+12=23, and 11+18=29 are all primes.
%t A377318 Select[Range[1, PrimePi[50000]], PrimeQ[Prime[#] + 6] && PrimeQ[Prime[#] + 12] && PrimeQ[Prime[#] + 18] &]
%t A377318 Select[Range[4500],AllTrue[Prime[#]+{0,6,12,18},PrimeQ]&] (* _Harvey P. Dale_, Jun 17 2025 *)
%o A377318 (PARI) for(k=1, primepi(50000), p = prime(k); if(isprime(p+6) && isprime(p+12) && isprime(p+18), print(k)))
%Y A377318 Cf. A000040, A000720, A023271.
%Y A377318 Subsequence of A377317.
%K A377318 nonn
%O A377318 1,1
%A A377318 _Kritsada Moomuang_, Oct 24 2024