OFFSET
1,1
COMMENTS
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).
REFERENCES
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 2.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..140
EXAMPLE
a(1) = prime(1^4) = 2,
a(2) = prime(2^4) = 53,
a(3) = prime(3^4) = 419, etc.
MATHEMATICA
Prime[Range[30]^4] (* Harvey P. Dale, Jun 07 2017 *)
PROG
(Magma) [NthPrime(n^4): n in [1..50] ]; // Vincenzo Librandi, Apr 22 2011
(PARI) a(n)=prime(n^4) \\ Charles R Greathouse IV, Oct 03 2013
(Sage) [nth_prime(n^4) for n in (1..30)] # G. C. Greubel, Dec 09 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Aug 14 2005
STATUS
approved