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

1,1

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

Formula

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

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

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

Sequence in context: A142477 A119112 A356488 * A265441 A354406 A119777

Adjacent sequences: A109788 A109789 A109790 * A109792 A109793 A109794

Keyword

nonn

Author

Jonathan Vos Post, Aug 14 2005

Status

approved