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 A125821 #23 Sep 18 2024 03:41:13
%S A125821 3,12,18,24,33,57,102,132,153,159,162,234,243,249,267,279,288,297,318,
%T A125821 348,423,432,444,447,477,489,519,528,552,564,579,627,684,687,717,774,
%U A125821 783,837,858,918,948,969,984,993
%N A125821 Numbers k for which 8*k+5 and 8*k+7 are twin primes.
%C A125821 From _Zak Seidov_, Apr 19 2008: (Start)
%C A125821 Proof that all numbers in this sequence are divisible by 3:
%C A125821 if n=(3k+1), then 8n+7=8(3k+1)+7=3(5+8 k) (composite)
%C A125821 if n=(3k+2), then 8n+5=8(3k+2)+5=3(7+8 k) (composite),
%C A125821 so if we require that both 8n+5 and 8n+7 are primes, then n=3k, hence all terms in this sequence are multiples of 3. QED. (End)
%H A125821 Harvey P. Dale, <a href="/A125821/b125821.txt">Table of n, a(n) for n = 1..1000</a>
%t A125821 Do[If[PrimeQ[8n + 5] && PrimeQ[8n + 7], Print[n]], {n, 1, 1000}]
%t A125821 Select[Range[3,6000,3],AllTrue[8#+{5,7},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Sep 14 2018 *)
%Y A125821 Cf. A001109.
%Y A125821 For a(n)/3 see A139404.
%Y A125821 Cf. A125822, A139402, A139404.
%K A125821 nonn
%O A125821 1,1
%A A125821 _Artur Jasinski_, Dec 10 2006