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Even-indexed primes: a(n) = prime(2n).
64

%I #41 Sep 08 2022 08:44:50

%S 3,7,13,19,29,37,43,53,61,71,79,89,101,107,113,131,139,151,163,173,

%T 181,193,199,223,229,239,251,263,271,281,293,311,317,337,349,359,373,

%U 383,397,409,421,433,443,457,463,479,491,503,521,541,557,569

%N Even-indexed primes: a(n) = prime(2n).

%C Also every second odd prime. - _Cino Hilliard_, Dec 02 2007

%C If n > 1, then a(n) is less than, and asymptotic to, the n-th Ramanujan prime R_n = A104272(n). Research questions on the difference R_n - a(n) are at A104272. - _Jonathan Sondow_, Dec 16 2013

%H Jens Kruse Andersen, <a href="/A031215/b031215.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A104272(n) - A233739(n). - _Jonathan Sondow_, Dec 16 2013

%F a(n) = A105720(n) - A161463(n). - _Torlach Rush_, May 31 2021

%p A031215 := n->ithprime(2*n);

%t Table[ Prime[ 2n], {n, 52}] (* _Robert G. Wilson v_, Dec 01 2013 *)

%o (Magma) [ NthPrime(2*n): n in [1..1000] ]; // _Vincenzo Librandi_, Apr 11 2011

%o (PARI) a(n)=prime(2*n) \\ _Charles R Greathouse IV_, Jul 02 2013

%Y Cf. A000040, A031368 (odd-indexed primes), A104272, A105720, A161463, A179740, A233739.

%K nonn,easy

%O 1,1

%A _Jeff Burch_