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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

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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 *)