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URL: https://oeis.org/A058009

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A058009
a(n) is obtained by applying the map k -> prime(k) n times, starting at n.
7
2, 5, 31, 277, 5381, 87803, 2269733, 50728129, 1559861749, 64988430769, 2428095424619, 119543903707171, 5519908106212193, 248761474969923757
OFFSET
1,1
LINKS
Piotr Miska and János T. Tóth, On interesting subsequences of the sequence of primes, arXiv:1908.10421 [math.NT], 2019. See DiagP.
Błażej Żmija, A note on primes with prime indices, arXiv:1909.12139 [math.NT], 2019.
EXAMPLE
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.
To get a(4): 4 -> 7 -> 17 -> 59 -> 277.
MAPLE
a:= n-> (ithprime@@n)(n):
seq(a(n), n=1..8); # Alois P. Heinz, Jun 21 2019
MATHEMATICA
Table[ Nest[ Prime, n, n ], {n, 1, 11} ]
PROG
(PARI) a(n) = my(k = n); for (j=1, n, k = prime(k); ); k; \\ Michel Marcus, Jan 01 2017
(Python)
from sympy import prime
def A058009(n):
k = n
for _ in range(n):
k = prime(k)
return k # Chai Wah Wu, Apr 06 2021
CROSSREFS
For composites, see A280327. - Matthew Campbell, Jan 01 2017
Sequence in context: A119242 A068145 A032112 * A056187 A056790 A192397
KEYWORD
nonn,hard,more
AUTHOR
Robert G. Wilson v, Nov 13 2000
EXTENSIONS
Edited by N. J. A. Sloane, Oct 30 2008 at the suggestion of R. J. Mathar
a(12)-a(13) from Donovan Johnson, Feb 17 2011
a(14) from Giovanni Resta, Sep 29 2019
a(13) corrected by Daniel Suteu, Jun 20 2021
STATUS
approved