

A109791


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


3



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
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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: A281227 A142477 A119112 * A265441 A119777 A176943
Adjacent sequences: A109788 A109789 A109790 * A109792 A109793 A109794


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Aug 14 2005


STATUS

approved



