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A058009 a(n) is obtained by applying the map k -> prime(k) n times, starting at n.

%I A058009 #47 Jun 26 2021 09:19:20
%S A058009 2,5,31,277,5381,87803,2269733,50728129,1559861749,64988430769,
%T A058009 2428095424619,119543903707171,5519908106212193,248761474969923757
%N A058009 a(n) is obtained by applying the map k -> prime(k) n times, starting at n.
%H A058009 Piotr Miska and János T. Tóth, <a href="https://arxiv.org/abs/1908.10421">On interesting subsequences of the sequence of primes</a>, arXiv:1908.10421 [math.NT], 2019. See DiagP.
%H A058009 Błażej Żmija, <a href="https://arxiv.org/abs/1909.12139">A note on primes with prime indices</a>, arXiv:1909.12139 [math.NT], 2019.
%e A058009 a(3) is 31 because the third prime is 5, the fifth prime is 11 and for the 3rd iteration, the eleventh prime is 31.
%e A058009 To get a(4): 4 -> 7 -> 17 -> 59 -> 277.
%p A058009 a:= n-> (ithprime@@n)(n):
%p A058009 seq(a(n), n=1..8);  # _Alois P. Heinz_, Jun 21 2019
%t A058009 Table[ Nest[ Prime, n, n ], {n, 1, 11} ]
%o A058009 (PARI) a(n) = my(k = n); for (j=1, n, k = prime(k);); k; \\ _Michel Marcus_, Jan 01 2017
%o A058009 (Python)
%o A058009 from sympy import prime
%o A058009 def A058009(n):
%o A058009     k = n
%o A058009     for _ in range(n):
%o A058009         k = prime(k)
%o A058009     return k # _Chai Wah Wu_, Apr 06 2021
%Y A058009 Cf. A000040, A006450, A049090, ...
%Y A058009 For composites, see A280327. - _Matthew Campbell_, Jan 01 2017
%K A058009 nonn,hard,more
%O A058009 1,1
%A A058009 _Robert G. Wilson v_, Nov 13 2000
%E A058009 Edited by _N. J. A. Sloane_, Oct 30 2008 at the suggestion of _R. J. Mathar_
%E A058009 a(12)-a(13) from _Donovan Johnson_, Feb 17 2011
%E A058009 a(14) from _Giovanni Resta_, Sep 29 2019
%E A058009 a(13) corrected by _Daniel Suteu_, Jun 20 2021