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%I A162864 #7 Dec 31 2024 18:09:33
%S A162864 6,12,18,30,36,42,60,72,108,180,192,240,270,312,420,432,462,600,660,
%T A162864 810,882,1092,1152,1290,1296,1302,1320,1620,1722,1872,2028,2112,2268,
%U A162864 2310,2340,2592,2688,2700,2790,2970,3000,3120,3258,3300,3360,3390,3528,3540
%N A162864 Integers n, divisible by six, for which t = (4^n - 5 * 2^n - 4 * 4^(n^2 - 2n) + 8 * 2^(n^2 - 2n)) / (4 * (n^3 - n)) is an integer
%C A162864 Then n - 1 and n + 1 are almost always a pair of twin primes, and the set of these should be an infinite subset of all twin primes.
%C A162864 If n - 1 and n + 1 are simultaneously composite, this occurs very rarely.
%H A162864 Harvey P. Dale, <a href="/A162864/b162864.txt">Table of n, a(n) for n = 1..100</a>
%t A162864 Select[6*Range[600],IntegerQ[(4^#-5*2^#-4*4^(#^2-2#)+8*2^(#^2-2#))/(4*(#^3-#))]&] (* _Harvey P. Dale_, Dec 31 2024 *)
%Y A162864 Cf. A001097
%Y A162864 Cf. A001359, A014574, A006512
%K A162864 easy,nonn
%O A162864 1,1
%A A162864 _Reikku Kulon_, Jul 15 2009

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