A280327 -id:A280327 - cp's OEIS frontend

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

Robert G. Wilson v, Nov 13 2000

			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.

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.

Cf. A000040, A006450, A049090, ...

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

a:= n-> (ithprime@@n)(n):
seq(a(n), n=1..8);  # Alois P. Heinz, Jun 21 2019

Table[ Nest[ Prime, n, n ], {n, 1, 11} ]

a(n) = my(k = n); for (j=1, n, k = prime(k);); k; \\ Michel Marcus, Jan 01 2017

from sympy import prime
def A058009(n):
    k = n
    for _ in range(n):
        k = prime(k)
    return k # Chai Wah Wu, Apr 06 2021

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

A377181 Rectangular array, by antidiagonals: (row 1) = r(1) = A002808 (composite numbers); (row n) = r(n) = A002808(r(n-1)) for n>=1.

Original entry on oeis.org

4, 6, 9, 8, 12, 16, 9, 15, 21, 26, 10, 16, 25, 33, 39, 12, 18, 26, 38, 49, 56, 14, 21, 28, 39, 55, 69, 78, 15, 24, 33, 42, 56, 77, 94, 106, 16, 25, 36, 49, 60, 78, 105, 125, 141, 18, 26, 38, 52, 69, 84, 106, 140, 164, 184, 20, 28, 39, 55, 74, 94, 115, 141, 183, 212, 236

Offset: 1

Clark Kimberling, Oct 19 2024

			 corner:
   4     6     8     9    10    12    14    15    16    18
   9    12    15    16    18    21    24    25    26    28
  16    21    25    26    28    33    36    38    39    42
  26    33    38    39    42    49    52    55    56    60
  39    49    55    56    60    69    74    77    78    84
  56    69    77    78    84    94   100   105   106   115
  78    94   105   106   115   125   133   140   141   152

Cf. A002808 (row 1), A050545 (row 2), A280327 (row 3), A006508 (column 1), A022450 (column 2), A023451 (column 3), A059981, A236356, A280327 (principal diagonal), A377173, A114577 (dispersion of the composite numbers).

c[n_] := c[n] = Select[Range[500], CompositeQ][[n]]
r[0] = Table[c[n], {n, 1, 10}]
r[n_] := r[n] = c[r[n - 1]]
Grid[Table[r[n], {n, 0, 6}]]  (* array *)
p[n_, k_] := r[n][[k]];
Table[p[n - k + 1, k], {n, 0, 9}, {k, n + 1, 1, -1}] // Flatten  (* sequence *)

A059981(n) = number of appearances of A002808(n).

cp's OEIS Frontend

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

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