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A060308
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Largest prime <= 2n.
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30
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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
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OFFSET
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1,1
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COMMENTS
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a(n) is the smallest k such that C(2n,n) divides k!. - Benoit Cloitre, May 30 2002
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
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LINKS
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FORMULA
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EXAMPLE
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n=1, 2n=2, p(1) = 2 = a(1) is the largest prime not exceeding 2.
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MAPLE
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seq (prevprime(2*i+1), i=1..256);
seq(max(op(select(isprime, [$n..2*n]))), n=1..66); # Peter Luschny, Mar 04 2011
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MATHEMATICA
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Table[Max[FactorInteger[(2n)!/(n!)^2]], {n, 1, 100}] (* Alexander Adamchuk, Jul 11 2006 *)
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PROG
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(Haskell)
(Magma) [NthPrime(#PrimesUpTo(2*n)): n in [2..100]]; // Vincenzo Librandi, Nov 25 2015
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CROSSREFS
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Apart from initial term, same as A060265.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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