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A065966 Numbers k such that phi(k) / 2 is prime. 10

%I #19 Feb 11 2020 15:28:21

%S 5,7,8,9,10,11,12,14,18,22,23,46,47,59,83,94,107,118,166,167,179,214,

%T 227,263,334,347,358,359,383,454,467,479,503,526,563,587,694,718,719,

%U 766,839,863,887,934,958,983,1006,1019,1126,1174,1187,1283,1307,1319

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

%C 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 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 Harry J. Smith, <a href="/A065966/b065966.txt">Table of n, a(n) for n = 1..1000</a>

%H 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 Numbers k such that A068212(k) = 2.

%e phi(46)/2 = 22/2 = 11, a prime.

%t Select[Range[1400],PrimeQ[EulerPhi[#]/2]&] (* _Harvey P. Dale_, Feb 11 2020 *)

%o (PARI) for(n=3,5000, if(isprime(eulerphi(n)/2),print1(n,",")))

%o (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 Cf. A000010, A005385, A005384, A066179, A006530, A052126, A068211, A068212.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Dec 08 2001

%E More terms from _Jason Earls_, Dec 09 2001

%E Edited by _Charles R Greathouse IV_, Mar 18 2010

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)