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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 May 6 02:46 EDT 2021. Contains 343579 sequences. (Running on oeis4.)