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%I A182481 #23 May 13 2013 01:54:19
%S A182481 1,1,1,3,1,2,1,4,2,1,3,1,4,5,2,2,1,1,2,2,7,5,1,3,1,2,5,16,2,1,7,1,1,5,
%T A182481 2,2,9,1,8,1,5,9,4,5,1,3,1,4,3,2,7,1,20,5,2,8,14,1,3,21,43,4,6,3,5,8,
%U A182481 4,9,2,1,3,1,14,15,9,30,1,4,22,7,20,21,9
%N A182481 a(n) is the least k such that 6*k*n-1 and 6*k*n+1 are twin primes, and a(n)=0, if such k does not exist.
%C A182481 Conjecture: a(n)>0; equivalently, for every n, the arithmetic progression {6*k*n-1} contains infinitely many lessers of twin primes (A001359).
%H A182481 Charles R Greathouse IV, <a href="/A182481/b182481.txt">Table of n, a(n) for n = 1..10000</a>
%t A182481 Table[k = 0; While[! (PrimeQ[6*k*n - 1] && PrimeQ[6*k*n + 1]), k++]; k, {n, 100}] (* _T. D. Noe_, May 02 2012 *)
%o A182481 (PARI) a(n)=my(k);n*=6;until(isprime(n*k++-1)&&isprime(n*k+1),);k \\ _Charles R Greathouse IV_, May 01 2012
%Y A182481 Cf. A001359, A006512, A014574, A001097, A077800, A002822.
%K A182481 nonn
%O A182481 1,4
%A A182481 _Vladimir Shevelev_, May 01 2012

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