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

2, 5, 31, 277, 5381, 87803, 2269733, 50728129, 1559861749, 64988430769, 2428095424619, 119543903707171, 5519908106212193, 248761474969923757

Offset: 1

Author

Robert G. Wilson v, Nov 13 2000

Keywords

• nonn
• hard
• more

Examples

			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.
		

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.

Crossrefs

Cf. A000040, A006450, A049090, ...

For composites, see A280327. - Matthew Campbell, Jan 01 2017

Programs

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} ]

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

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