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 A049481 #47 Mar 15 2025 11:29:42
%S A049481 7,11,13,17,23,29,31,37,41,43,53,59,67,71,73,79,83,97,101,107,109,127,
%T A049481 137,149,151,163,167,181,193,197,199,211,227,233,239,241,251,263,277,
%U A049481 281,283,307,317,337,349,353,359,367,379,389,401,409,419,431,433,449
%N A049481 Primes p such that p + 30 is also prime.
%C A049481 30 = A002110(3) is the 3rd primorial number.
%C A049481 p and p+30 are not necessarily consecutive primes. Initial segment of A045320 is identical, but 113 is not in this sequence because 113 + 30 = 143 is divisible by 13.
%H A049481 Harvey P. Dale, <a href="/A049481/b049481.txt">Table of n, a(n) for n = 1..10000</a>
%H A049481 Hugo Pfoertner, <a href="/A049481/a049481.png">Observed ratio n*log(a(n))/pi(a(n))</a> for n=10^7..5.6*10^9 with a conjectured extrapolation for large n (2024).
%F A049481 Assuming Polignac's conjecture and the first Hardy-Littlewood conjecture: Limit_{n->oo} n*log(a(n))/primepi(a(n)) = (16/3)*A005597 = 3.52086... . - _Alain Rocchelli_, Oct 29 2024
%e A049481 7 is a term since it is prime and 7 + 30 = 37 is also prime.
%t A049481 lst={};Do[p=Prime[n];If[PrimeQ[p+30],AppendTo[lst,p]],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 04 2009 *)
%t A049481 Select[Prime[Range[100]],PrimeQ[#+30]&] (* _Harvey P. Dale_, Apr 28 2012 *)
%o A049481 (PARI) isok(p) = isprime(p) && isprime(p + 30); \\ _Amiram Eldar_, Mar 15 2025
%Y A049481 Cf. A002110, A045320, A005597.
%Y A049481 Cf. A001359, A023201, A049482, A049483, A049484, A049485, A154114.
%K A049481 nonn
%O A049481 1,1
%A A049481 _Labos Elemer_