A109791 a(n) = prime(n^4).

2, 53, 419, 1619, 4637, 10627, 21391, 38873, 65687, 104729, 159521, 233879, 331943, 459341, 620201, 821641, 1069603, 1370099, 1731659, 2160553, 2667983, 3260137, 3948809, 4742977, 5653807, 6691987, 7867547, 9195889, 10688173, 12358069

Offset: 1

Author

Jonathan Vos Post, Aug 14 2005

Keywords

• nonn

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).

Examples

			a(1) = prime(1^4) = 2,
a(2) = prime(2^4) = 53,
a(3) = prime(3^4) = 419, etc.
		

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

Crossrefs

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

Programs

Magma

[NthPrime(n^4): n in [1..50] ]; // Vincenzo Librandi, Apr 22 2011

Mathematica

Prime[Range[30]^4] (* Harvey P. Dale, Jun 07 2017 *)

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

Formula

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