A344946 x -> prime(x) iterated prime(n) times, evaluated at n.

3, 11, 709, 167449, 88362852307, 156740126985437, 1172447586903041169661

Offset: 1

Author

Paolo Xausa, Jun 03 2021

Keywords

• nonn
• more
• hard

Examples

			a(1) = prime(prime(1)) = 3.
a(2) = prime(prime(prime(2))) = 11.
a(3) = prime(prime(prime(prime(prime(3))))) = 709.
		

Crossrefs

Cf. A000040, A058009.

Programs

Mathematica

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

PARI

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

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

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}.

Extensions

a(7) from Jinyuan Wang, Jul 12 2021