OFFSET
1,1
COMMENTS
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.)
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
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1000
André Hernández-Espiet, Reyes M. Ortiz-Albino, On the Characterization of tau(n)-Atoms, arXiv:1905.02834 [math.NT], 2019. See Proposition 3.1.
FORMULA
Numbers k such that A068212(k) = 2.
EXAMPLE
phi(46)/2 = 22/2 = 11, a prime.
MATHEMATICA
Select[Range[1400], PrimeQ[EulerPhi[#]/2]&] (* Harvey P. Dale, Feb 11 2020 *)
PROG
(PARI) for(n=3, 5000, if(isprime(eulerphi(n)/2), print1(n, ", ")))
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Dec 08 2001
EXTENSIONS
More terms from Jason Earls, Dec 09 2001
Edited by Charles R Greathouse IV, Mar 18 2010
STATUS
approved