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

1,1

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.

Links

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

Example

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.

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}]

Prog

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

Crossrefs

Cf. A000010, A000040, A000079, A236374.

Sequence in context: A310225 A310226 A062731 * A310227 A310228 A310229

Adjacent sequences: A236372 A236373 A236374 * A236376 A236377 A236378

Keyword

nonn

Author

Zhi-Wei Sun, Jan 24 2014

Status

approved