A276650 Primes of the form prime(k)^k - PrimePi(k).

2, 2399, 1801152661459, 73885357344138503765443

Offset: 1

Author

Robert C. Lyons, Sep 09 2016

Keywords

• nonn
• more

Comments

Searched up to k = 1000.

No additional entries up to k = 5000. - Ethan Beihl, Oct 15 2016

No additional entries up to k = 15000. - Tyler Busby, Mar 12 2024

Examples

			2 is in the sequence because 2 is prime and 2 = prime(1)^1 - PrimePi(1) = 2^1 - 0.
2399 is in the sequence because 2399 is prime and 2399 = prime(4)^4 - PrimePi(4) = 7^4 - 2.
1801152661459 is in the sequence because 1801152661459 is prime and 1801152661459 = prime(9)^9 - PrimePi(9) = 23^9 - 4.
73885357344138503765443 is in the sequence because 73885357344138503765443 is prime and 73885357344138503765443 = prime(14)^14 - PrimePi(14) = 43^14 - 6.
		

Links

• Farideh Firoozbakht, Prime Curios: Prime(14)^14 - pi(14) is prime.

Crossrefs

Cf. A000720, A062457.

Programs

Mathematica

Select[Map[Prime[#]^# - PrimePi@ # &, Range@ 1500], PrimeQ] (* Michael De Vlieger, Sep 26 2016 *)

SageMath

max_n = 20
seq = []
for n in range(1, max_n+1):
    p = nth_prime(n)^n - prime_pi(n)
    if is_prime(p):
        seq.append(p)
print(seq)