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A236375 Positive integers m with 2^(m-1)*phi(m) - 1 prime, where phi(.) is Euler's totient function. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 27 19:04 EDT 2020. Contains 337388 sequences. (Running on oeis4.)