A087865 Prime numbers of the form primepi(3^m), for some integer m.

2, 53, 16097, 120739, 334349, 18703411700669

Offset: 1

Author

Cino Hilliard, Oct 27 2003

Keywords

• nonn
• more
• hard

Comments

These are the prime terms in A055729.

Crossrefs

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

Programs

Mathematica

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

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) }

Python

from itertools import islice
from sympy import isprime, primepi
def A087865_gen(): # generator of terms
    k = 1
    while True:
        k *= 3
        if isprime(p:=primepi(k)):
            yield p
A087865_list = list(islice(A087865_gen(),5)) # Chai Wah Wu, Jun 06 2024

Extensions

a(6) added by David Baugh, Mar 17 2015