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Search: id:A109791
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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
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OFFSET
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1,1
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COMMENT
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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
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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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FORMULA
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A000040(A000290(n)) for n>0. A011757(n^2).
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EXAMPLE
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a(1) = prime[1^4] = prime[1] = 2,
a(2) = prime[2^4] = prime[16] = 53,
a(3) = prime[3^4] = prime[81] = 419,
a(4) = prime[4^4] = prime[256] = 1619,
a(5) = prime[5^4] = prime[625] = 4637,
a(6) = prime[6^4] = prime[1296] = 10627,
a(7) = prime[7^4] = prime[2401] = 21391,
a(8) = prime[8^4] = prime[4096] = 38873,
a(9) = prime[9^4] = prime[6561] = 65687,
a(10) = prime[10^4] = prime[10000] = 104729.
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CROSSREFS
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Cf. A000040, A000290, A011757, A109724, A109770.
Sequence in context: A123005 A142477 A119112 this_sequence A119777 A087865 A083471
Adjacent sequences: A109788 A109789 A109790 this_sequence A109792 A109793 A109794
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 14 2005
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