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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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).
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REFERENCES
| G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 2.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..140
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FORMULA
| a(n) = A000040(A000290(n)) for n>0.
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EXAMPLE
| a(1) = prime(1^4) = 2,
a(2) = prime(2^4) = 53,
a(3) = prime(3^4) = 419, etc.
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PROG
| (MAGMA) [NthPrime(n^4): n in [1..50] ]; // Vincenzo Librandi, Apr 22 2011
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CROSSREFS
| Cf. A000040, A000290, A011757, A109724, A109770.
Sequence in context: A123005 A142477 A119112 * A119777 A176943 A176946
Adjacent sequences: A109788 A109789 A109790 * A109792 A109793 A109794
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KEYWORD
| nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 14 2005
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