cp's OEIS Frontend

A065966 Numbers k such that phi(k) / 2 is prime.

%I A065966 #19 Feb 11 2020 15:28:21
%S A065966 5,7,8,9,10,11,12,14,18,22,23,46,47,59,83,94,107,118,166,167,179,214,
%T A065966 227,263,334,347,358,359,383,454,467,479,503,526,563,587,694,718,719,
%U A065966 766,839,863,887,934,958,983,1006,1019,1126,1174,1187,1283,1307,1319
%N A065966 Numbers k such that phi(k) / 2 is prime.
%C A065966 This is probably an infinite sequence, but a proof would be nice. Are there infinitely many consecutive terms of the sequence which are also consecutive integers? (For example, 7, 8 and 46, 47.)
%C A065966 Apart from 8, 9, 12 and 18, all the terms of the sequence are safe primes or twice safe primes. It is not known if there are infinitely many safe primes (cf. A005385, A005384). For consecutive terms of the sequence which are also consecutive integers see A066179. - _Vladeta Jovovic_, Dec 16 2001
%H A065966 Harry J. Smith, <a href="/A065966/b065966.txt">Table of n, a(n) for n = 1..1000</a>
%H A065966 André Hernández-Espiet, Reyes M. Ortiz-Albino, <a href="https://arxiv.org/abs/1905.02834">On the Characterization of tau(n)-Atoms</a>, arXiv:1905.02834 [math.NT], 2019. See Proposition 3.1.
%F A065966 Numbers k such that A068212(k) = 2.
%e A065966 phi(46)/2 = 22/2 = 11, a prime.
%t A065966 Select[Range[1400],PrimeQ[EulerPhi[#]/2]&] (* _Harvey P. Dale_, Feb 11 2020 *)
%o A065966 (PARI) for(n=3,5000, if(isprime(eulerphi(n)/2),print1(n,",")))
%o A065966 (PARI) { n=0; for (m=3, 10^9, if (isprime(eulerphi(m)/2), write("b065966.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Nov 05 2009
%Y A065966 Cf. A000010, A005385, A005384, A066179, A006530, A052126, A068211, A068212.
%K A065966 nonn
%O A065966 1,1
%A A065966 _Joseph L. Pe_, Dec 08 2001
%E A065966 More terms from _Jason Earls_, Dec 09 2001
%E A065966 Edited by _Charles R Greathouse IV_, Mar 18 2010