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A344946 x -> prime(x) iterated prime(n) times, evaluated at n. 0
3, 11, 709, 167449, 88362852307, 156740126985437, 1172447586903041169661 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..7.

FORMULA

a(n) = prime^{prime(n)}(n), with prime^{0}(n) = n and prime^{k}(n) = prime(prime^{k-1}(n)) for 1 <= k <= prime(n).

a(n) = prime(prime(...(n))) {prime(n) times}.

EXAMPLE

a(1) = prime(prime(1)) = 3.

a(2) = prime(prime(prime(2))) = 11.

a(3) = prime(prime(prime(prime(prime(3))))) = 709.

MATHEMATICA

nterms=6; Table[Nest[Prime[#]&, n, Prime[n]], {n, nterms}]

PROG

(Python)

from sympy import prime

def a(n):

  iter = pn = prime(n)

  for i in range(1, pn): iter = prime(iter)

  return iter

print([a(n) for n in range(1, 6)]) # Michael S. Branicky, Jun 03 2021

(PARI) a(n) = my(p = n); for (k=1, prime(n), p=prime(p)); p; \\ Michel Marcus, Jun 03 2021

CROSSREFS

Cf. A000040, A058009.

Sequence in context: A337415 A264725 A088579 * A006938 A124984 A287432

Adjacent sequences:  A344943 A344944 A344945 * A344947 A344948 A344949

KEYWORD

nonn,more,hard

AUTHOR

Paolo Xausa, Jun 03 2021

EXTENSIONS

a(7) from Jinyuan Wang, Jul 12 2021

STATUS

approved

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Last modified October 17 16:03 EDT 2021. Contains 348065 sequences. (Running on oeis4.)