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Primes at large indices: a(n) = prime(n!).
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%I #35 Dec 27 2024 13:30:19

%S 2,2,3,13,89,659,5443,49033,484037,5222429,61194647,774825383,

%T 10552185239,153903050137,2394322471421,39588599419319,

%U 693389445083107,12826386978604427,249902442548157673,5115640857307591139,109776797549312197217,2464348772728229970857

%N Primes at large indices: a(n) = prime(n!).

%H Andrew Booker, <a href="https://t5k.org/nthprime/index.php#n-th">Nth Prime Page</a>.

%F a(n) = A000040(A000142(n)).

%p seq(ithprime(factorial(n)),n=0..10); # _Muniru A Asiru_, Dec 07 2018

%t Array[Prime[#!] &, 16, 0] (* _Michael De Vlieger_, Dec 06 2018 *)

%o (PARI) a(n) = prime(n!)

%o (Magma) [(NthPrime(Factorial(n))): n in [0..11]]; // _Vincenzo Librandi_, Dec 07 2018

%o (Python)

%o from sympy import prime, factorial

%o for n in range(0,14): print(prime(factorial(n))) # _Stefano Spezia_, Dec 07 2018

%Y Cf. A000040, A000142, A033844.

%K hard,nonn

%O 0,1

%A _Labos Elemer_, Jul 09 2001

%E a(15)-a(19) from _Jens Kruse Andersen_, May 08 2010

%E a(20)-a(21) from _Henri Lifchitz_, Sep 09 2014