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%I A109791 #21 Sep 08 2022 08:45:19
%S A109791 2,53,419,1619,4637,10627,21391,38873,65687,104729,159521,233879,
%T A109791 331943,459341,620201,821641,1069603,1370099,1731659,2160553,2667983,
%U A109791 3260137,3948809,4742977,5653807,6691987,7867547,9195889,10688173,12358069
%N A109791 a(n) = prime(n^4).
%C A109791 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).
%D A109791 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 2.
%H A109791 Vincenzo Librandi, <a href="/A109791/b109791.txt">Table of n, a(n) for n = 1..140</a>
%F A109791 a(n) = A000040(A000583(n)) for n > 0.
%e A109791 a(1) = prime(1^4) = 2,
%e A109791 a(2) = prime(2^4) = 53,
%e A109791 a(3) = prime(3^4) = 419, etc.
%t A109791 Prime[Range[30]^4] (* _Harvey P. Dale_, Jun 07 2017 *)
%o A109791 (Magma) [NthPrime(n^4): n in [1..50] ]; // _Vincenzo Librandi_, Apr 22 2011
%o A109791 (PARI) a(n)=prime(n^4) \\ _Charles R Greathouse IV_, Oct 03 2013
%o A109791 (Sage) [nth_prime(n^4) for n in (1..30)] # _G. C. Greubel_, Dec 09 2018
%Y A109791 Cf. A000040, A000583, A011757, A109724, A109770.
%K A109791 nonn
%O A109791 1,1
%A A109791 _Jonathan Vos Post_, Aug 14 2005

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