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a(n) = smallest k such that (6*k*n-3)*2^n-1 is prime, or 0 if no such prime exists.
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%I #28 Jul 02 2017 08:02:31

%S 1,2,2,2,1,1,0,1,1,1,1,4,6,6,0,15,2,8,3,1,9,4,3,14,1,0,3,0,1,2,1,3,4,

%T 25,0,1,24,2,17,22,2,4,16,2,13,9,17,17,0,10,17,3,6,34,0,1,69,5,26,8,4,

%U 3,3,8,16,19,3,5,5,0,18,8,75,5,0,1,0,37,19,14,85,4,4,47

%N a(n) = smallest k such that (6*k*n-3)*2^n-1 is prime, or 0 if no such prime exists.

%C For some n (6*k*n-3)*2^n-1 is composite for any k.

%C For n=15+20*j, n=7+21*j, n=77+110*j, n=26+156*j, n=266+342*j, n=261+812*j, n=2368+1332*j, n=477+2756*j, n=2183+3422*j and more others (6*k*n-3)*2^n-1 is always composite for any k and any j.

%C For n=4390+187892*j, (6*k*n-3)*2^n-1 is always divisible by one of the 82 primes between 5 and 443, 4390=10*439 and 187892=438*439.

%C For n=6152+596744*j, (6*k*n-3)*2^n-1 is always divisible by one of the 134 primes between 3 and 773, 6152=8*769 and 596744=768*769.

%C For n=11*1229+1228*1229*j, (6*n*k-3)*2^n-1 is always divisible by one of the 199 primes between 3 and 1231 except 11.

%C For n=27*1399+1398*1399*j, (6*n*k-3)*2^n-1 is always divisible by one of the 220 primes between 3 and 1409.

%C For n=5*11*1619+1618*1619*j, (6*n*k-3)*2^n-1 is always divisible by one of the 253 primes between 5 and 1621 except 11.

%H Pierre CAMI, <a href="/A288160/b288160.txt">Table of n, a(n) for n = 1..9000</a>

%Y Cf. A285808.

%K nonn

%O 1,2

%A _Pierre CAMI_, Jun 19 2017