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a(1) = prime(1), a(2) = prime(prime( a(1) )), a(3) = prime(prime(prime( a(2) ))), a(4) = prime(prime(prime(prime( a(3) )))), etc.
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%I #15 Apr 03 2023 10:36:10

%S 2,5,127,648391,2428095424619,75063692618249,2586559730396077,

%T 98552043847093519

%N a(1) = prime(1), a(2) = prime(prime( a(1) )), a(3) = prime(prime(prime( a(2) ))), a(4) = prime(prime(prime(prime( a(3) )))), etc.

%H A. Booker, <a href="https://t5k.org/nthprime">The Nth Prime Page</a>

%p ithprime(1); ithprime(ithprime(%)); ithprime(ithprime(ithprime(%))); ithprime(ithprime(ithprime(ithprime(%))));

%t a[1] = 2; a[n_] := Nest[Prime, a[n - 1], n]; Table[ a[n], {n, 5}] (* _Robert G. Wilson v_, Dec 24 2004 *)

%Y Cf. A007097, the primeth recurrence.

%K nonn

%O 1,1

%A _Jorge Coveiro_, Apr 17 2004

%E a(5) from _Robert G. Wilson v_, Dec 24 2004

%E a(6)-a(8) from _Zak Seidov_, Sep 04 2016