%I #21 Sep 08 2022 08:45:19

%S 2,53,419,1619,4637,10627,21391,38873,65687,104729,159521,233879,

%T 331943,459341,620201,821641,1069603,1370099,1731659,2160553,2667983,

%U 3260137,3948809,4742977,5653807,6691987,7867547,9195889,10688173,12358069

%N a(n) = prime(n^4).

%C Since the prime number theorem is the statement that prime[n] ~ n * log n as n -> infinity [Hardy and Wright, page 10] we have a(n) = prime(n^4) is asymptotically (n^4)*log(n^4) = 4*(n^4)*log(n).

%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 2.

%H Vincenzo Librandi, <a href="/A109791/b109791.txt">Table of n, a(n) for n = 1..140</a>

%F a(n) = A000040(A000583(n)) for n > 0.

%e a(1) = prime(1^4) = 2,

%e a(2) = prime(2^4) = 53,

%e a(3) = prime(3^4) = 419, etc.

%t Prime[Range[30]^4] (* _Harvey P. Dale_, Jun 07 2017 *)

%o (Magma) [NthPrime(n^4): n in [1..50] ]; // _Vincenzo Librandi_, Apr 22 2011

%o (PARI) a(n)=prime(n^4) \\ _Charles R Greathouse IV_, Oct 03 2013

%o (Sage) [nth_prime(n^4) for n in (1..30)] # _G. C. Greubel_, Dec 09 2018

%Y Cf. A000040, A000583, A011757, A109724, A109770.

%K nonn

%O 1,1

%A _Jonathan Vos Post_, Aug 14 2005