A236375 Positive integers m with 2^(m-1)*phi(m) - 1 prime, where phi(.) is Euler's totient function.

3, 7, 12, 15, 18, 31, 42, 108, 124, 140, 143, 155, 207, 327, 386, 463, 514, 823, 925, 1035, 1393, 1425, 2425, 3873, 5091, 5314, 5946, 12813, 14198, 15823, 19932, 22747, 37989, 38772

Offset: 1

Author

Zhi-Wei Sun, Jan 24 2014

Keywords

• nonn

Comments

According to the conjecture in A236374, this sequence should have infinitely many terms.

The prime 2^(a(34)-1)*phi(a(34)) - 1 = 2^(38771)*12888 - 1 has 11676 decimal digits.

Examples

			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.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..34

Crossrefs

Cf. A000010, A000040, A000079, A236374.

Programs

Mathematica

q[m_]:=PrimeQ[2^(m-1)*EulerPhi[m]-1]
n=0;Do[If[q[m],n=n+1;Print[n," ",m]],{m,1,10000}]

PARI

s=[]; for(m=1, 1000, if(isprime(2^(m-1)*eulerphi(m)-1), s=concat(s, m))); s \\ Colin Barker, Jan 24 2014