A060308 Largest prime <= 2n.

2, 3, 5, 7, 7, 11, 13, 13, 17, 19, 19, 23, 23, 23, 29, 31, 31, 31, 37, 37, 41, 43, 43, 47, 47, 47, 53, 53, 53, 59, 61, 61, 61, 67, 67, 71, 73, 73, 73, 79, 79, 83, 83, 83, 89, 89, 89, 89, 97, 97, 101, 103, 103, 107, 109, 109, 113, 113, 113, 113, 113, 113, 113, 127, 127, 131

Offset: 1

Author

Labos Elemer, Mar 27 2001

Keywords

• nonn
• easy

Comments

a(n) is the smallest k such that C(2n,n) divides k!. - Benoit Cloitre, May 30 2002

a(n) is largest prime factor of C(2n,n) = (2n)!/(n!)^2. - Alexander Adamchuk, Jul 11 2006

a(n) is also the largest prime in the interval [n,2n]. - Peter Luschny, Mar 04 2011

Odd prime p repeats (q-p)/2 times, where q > p is the next prime. In particular, every lesser of twin primes (A001359) occurs 1 time, every lesser more than 3 of cousin primes (A023200) occurs 2 times, etc. - Vladimir Shevelev, Mar 12 2012

Examples

			n=1, 2n=2, p(1) = 2 = a(1) is the largest prime not exceeding 2.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Apart from initial term, same as A060265.

Cf. A007917 (largest prime <= n), A005843 (2n).

Cf. A020482, A049653, A060266, A060267, A060268, A060264.

Programs

Haskell

a060308 = a007917 . a005843 -- Reinhard Zumkeller, May 25 2013

Magma

[NthPrime(#PrimesUpTo(2*n)): n in [2..100]]; // Vincenzo Librandi, Nov 25 2015

Maple

seq (prevprime(2*i+1), i=1..256);
seq(max(op(select(isprime,[$n..2*n]))),n=1..66); # Peter Luschny, Mar 04 2011

Mathematica

Table[Max[FactorInteger[(2n)!/(n!)^2]],{n,1,100}] (* Alexander Adamchuk, Jul 11 2006 *)
NextPrime[2*Range[80]+1,-1] (* Harvey P. Dale, Apr 23 2017 *)

PARI

a(n)=precprime(2*n) \\ Charles R Greathouse IV, May 24 2013

Formula

a(n) = Max[FactorInteger[(2n)!/(n!)^2]]. - Alexander Adamchuk, Jul 11 2006

a(n) = A006530(A000142(2*n)) and a(n) = A006530(A056040(2*n)). - Peter Luschny, Mar 04 2011

a(n) ~ 2*n as n tends to infinity. - Vladimir Shevelev, Mar 12 2012

a(n) = A007917(A005843(n)) = A226078(n, A067434(n)). - Reinhard Zumkeller, May 25 2013

Extensions

More terms from Alexander Adamchuk, Jul 11 2006