%I #31 Jun 06 2024 14:18:53

%S 2,53,16097,120739,334349,18703411700669

%N Prime numbers of the form primepi(3^m), for some integer m.

%C These are the prime terms in A055729.

%t Select[ Table[ PrimePi[ 3^n], {n, 0, 49}], PrimeQ@# &] (* _Robert G. Wilson v_, Feb 25 2010 *)

%o (PARI) primeslessxn2(n, p) = /*primes < p^n if prime */ { sr=0; for(x=0, n, y=primepi(p^x); if(y<>0, sr+=1.0/y); if(isprime(y), print1(y", ")); ); print(); print(sr) }

%o (Python)

%o from itertools import islice

%o from sympy import isprime, primepi

%o def A087865_gen(): # generator of terms

%o k = 1

%o while True:

%o k *= 3

%o if isprime(p:=primepi(k)):

%o yield p

%o A087865_list = list(islice(A087865_gen(),5)) # _Chai Wah Wu_, Jun 06 2024

%Y Cf. A055729 (number of primes <= 3^n).

%K nonn,more,hard

%O 1,1

%A _Cino Hilliard_, Oct 27 2003

%E a(6) added by _David Baugh_, Mar 17 2015