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%I #15 Jan 24 2014 10:23:38
%S 3,7,12,15,18,31,42,108,124,140,143,155,207,327,386,463,514,823,925,
%T 1035,1393,1425,2425,3873,5091,5314,5946,12813,14198,15823,19932,
%U 22747,37989,38772
%N Positive integers m with 2^(m-1)*phi(m) - 1 prime, where phi(.) is Euler's totient function.
%C According to the conjecture in A236374, this sequence should have infinitely many terms.
%C The prime 2^(a(34)-1)*phi(a(34)) - 1 = 2^(38771)*12888 - 1 has 11676 decimal digits.
%H Zhi-Wei Sun, <a href="/A236375/b236375.txt">Table of n, a(n) for n = 1..34</a>
%e a(1) = 3 since neither 2^(1-1)*phi(1) - 1 = 0 nor 2^(2-1)*phi(2) - 1 = 1 is prime, but 2^(3-1)*phi(3) - 1 = 4*2 - 1 = 7 is prime.
%t q[m_]:=PrimeQ[2^(m-1)*EulerPhi[m]-1]
%t n=0;Do[If[q[m],n=n+1;Print[n," ",m]],{m,1,10000}]
%o (PARI) s=[]; for(m=1, 1000, if(isprime(2^(m-1)*eulerphi(m)-1), s=concat(s, m))); s \\ _Colin Barker_, Jan 24 2014
%Y Cf. A000010, A000040, A000079, A236374.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Jan 24 2014
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