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A276650 Primes of the form prime(n)^n - PrimePi(n). 0

%I

%S 2,2399,1801152661459,73885357344138503765443

%N Primes of the form prime(n)^n - PrimePi(n).

%C Searched up to n = 1000.

%C Searched up to n = 5000, and found no additional entries. - _Ethan Beihl_, Oct 15 2016

%H Farideh Firoozbakht, <a href="https://primes.utm.edu/curios/page.php/14.html">Prime Curios: Prime(14)^14 - pi(14) is prime</a>

%e 2 is in the sequence because 2 is prime and 2 = prime(1)^1 - PrimePi(1) = 2^1 - 0.

%e 2399 is in the sequence because 2399 is prime and 2399 = prime(4)^4 - PrimePi(4) = 7^4 - 2.

%e 1801152661459 is in the sequence because 1801152661459 is prime and 1801152661459 = prime(9)^9 - PrimePi(9) = 23^9 - 4.

%e 73885357344138503765443 is in the sequence because 73885357344138503765443 is prime and 73885357344138503765443 = prime(14)^14 - PrimePi(14) = 43^14 - 6.

%t Select[Map[Prime[#]^# - PrimePi@ # &, Range@ 1500], PrimeQ] (* _Michael De Vlieger_, Sep 26 2016 *)

%o (Sage)

%o max_n = 20

%o seq = []

%o for n in range(1, max_n+1):

%o p = nth_prime(n)^n - prime_pi(n)

%o if is_prime(p):

%o seq.append(p)

%o print seq

%Y Cf. A000720, A062457.

%K nonn,more

%O 1,1

%A _Robert C. Lyons_, Sep 09 2016

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Last modified October 22 07:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)