A237659 - OEIS

%I #23 Apr 30 2018 11:14:33

%S 17,41,59,109,127,157,353,367,709,1153,1787,3319,3407,3911,5851,6037,

%T 6217,6469,8389,9103,9319,10663,13709,14107,14591,15683,18433,19463,

%U 19577,20107,21727,23209,27809,29383,32797,35023,36251,36599,38351,39239

%N Primes p with pi(p) and pi(p^2) both prime, where pi(.) is given by A000720.

%C This is a subsequence of A237658.

%C Conjecture: The sequence has infinitely many terms.

%H Chai Wah Wu, <a href="/A237659/b237659.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..600 from Zhi-Wei Sun)

%e a(1) = 17 with pi(17) = 7 and pi(17^2) = 61 both prime.

%e a(2) = 41 with pi(41) = 13 and pi(41^2) = 263 both prime.

%t p[m_]:=PrimeQ[PrimePi[m^2]]

%t n=0;Do[If[p[Prime[Prime[k]]],n=n+1;Print[n," ",Prime[Prime[k]]]],{k,1,1000}]

%Y Cf. A000040, A000290, A000720, A006450, A038107, A237656, A237657, A237658.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Feb 11 2014