OFFSET
1,1
COMMENTS
Apparently the sequence is infinite, but I have no proof. There are many n-ples of consecutives: (15,16)-(20,21)-(24,25,26)-(537,538)-(1436,1437)-...-(30236-30237)
This sequence is infinite if and only if there are infinitely many primes of the form 2p+1 or 4p+1 with prime p. - Charles R Greathouse IV, Feb 04 2013
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) >> n log^2 n. - Charles R Greathouse IV, Feb 04 2013
EXAMPLE
a(5) = 21 since pi(21)/4 = 12/4 = 3 is prime.
MATHEMATICA
Select[Range[800], PrimeQ[EulerPhi[#]/4]&] (* Harvey P. Dale, Feb 11 2015 *)
PROG
(PARI) is(n)=n=eulerphi(n); n%4==0 && isprime(n/4) \\ Charles R Greathouse IV, Feb 04 2013
(PARI) is(n)=if(n<51, n=eulerphi(n); n%4==0 && isprime(n/4), my(v=[3, 4, 6]); for(i=1, #v, if(n%(2*v[i])==v[i]&&gcd(n/v[i], v[i])==1&&isprime(n/v[i])&&isprime(eulerphi(n)/4), return(1))); if(n%4==2, n/=2); n%4==1&&isprime(n)&&isprime(n\4)) \\ Charles R Greathouse IV, Feb 04 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Carmine Suriano, Sep 14 2010
STATUS
approved