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%I #13 Sep 08 2022 08:45:19
%S 4,270,37200,57900,63690,80910,150960,256470,367230,405990,577980,
%T 641580,706920,1479480,1547880,1730580,2026470,2081160,2210280,
%U 2374530,2423040,2583240,3090780,3437220,3510810,4140420,4441530,4847460
%N Values of k such that k - 1 and k + 1 are twin primes and 3*k^9 - 1 and 3*k^9 + 1 are also twin primes.
%H Amiram Eldar, <a href="/A108134/b108134.txt">Table of n, a(n) for n = 1..1000</a>
%e 270 is in the sequence because 270 - 1 = 269 and 270 + 1 = 271 are twin primes and 3*270^9 - 1 = 22876792454960999999999 and 3*270^9 + 1 = 22876792454961000000001 are also twin primes.
%t fQ[n_] := Block[{p = n + 1}, PrimeQ[p + 1] && PrimeQ[3p^9 - 1] && PrimeQ[3p^9 + 1]]; Select[ Prime[ Range[408581]], fQ[ # ] &] + 1 (* _Robert G. Wilson v_, Jun 09 2005 *)
%o (Magma) twin:=func<p|IsPrime(p-1) and IsPrime(p+1)>; [k:k in [2..5000000]| twin(k) and twin(3*k^9)]; // _Marius A. Burtea_, Jan 03 2020
%K nonn
%O 1,1
%A _Ray G. Opao_, Jun 05 2005
%E More terms from _Robert G. Wilson v_, Jun 09 2005