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%I #15 Sep 14 2018 19:28:55
%S 3,12,18,24,33,57,102,132,153,159,162,234,243,249,267,279,288,297,318,
%T 348,423,432,444,447,477,489,519,528,552,564,579,627,684,687,717,774,
%U 783,837,858,918,948,969,984,993
%N Numbers n for which 8n+5 and 8n+7 are twin primes.
%C Proof that all numbers in this sequence are divisible by 3 (Zak Seidov Apr 19 2008:
%C if n=(3k+1), then 8n+7=8(3k+1)+7=3(5+8 k) (composite)
%C if n=(3k+2), then 8n+5=8(3k+2)+5=3(7+8 k) (composite),
%C so if we require that both 8n+5 and 8n+7 are primes, then n=3k, hence all terms in A125821 are multiples of 3. QED.
%H Harvey P. Dale, <a href="/A125821/b125821.txt">Table of n, a(n) for n = 1..1000</a>
%t Do[If[PrimeQ[8n + 5] && PrimeQ[8n + 7], Print[n]], {n, 1, 1000}]
%t 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 Cf. A001109.
%Y For a(n)/3 see A139404.
%Y Cf. A125822, A139402, A139404.
%K nonn
%O 1,1
%A _Artur Jasinski_, Dec 10 2006
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