

A120303


Largest prime factor of Catalan number A000108(n).


2



2, 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, 131
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OFFSET

2,1


COMMENTS

All prime numbers (except 3) are present in this sequence in their natural order with repetition. The number of repetitions is equal to A028334(n): differences between consecutive primes, divided by 2.  Alexander Adamchuk, Jul 30 2006
For p>3 a((p+1)/2) = p and all a(n) = p for n >= (p+1)/2 until the first occurrence of the next prime q = NextPrime(p) at a((q+1)/2) = q.  Alexander Adamchuk, Dec 27 2013


LINKS

Table of n, a(n) for n=2..67.


FORMULA

a(n) = A060308(n) = A060265(n) for n>2.
a(n) = A006530(A000108(n)).  Michel Marcus, Nov 14 2015


MATHEMATICA

Table[Max[FactorInteger[(2n)!/n!/(n+1)! ]], {n, 2, 100}]
FactorInteger[CatalanNumber[#]][[1, 1]]&/@Range[2, 70] (* Harvey P. Dale, May 02 2017 *)


PROG

(PARI) a(n) = vecmax(factor(binomial(2*n, n)/(n+1))[, 1]); \\ Michel Marcus, Nov 14 2015
(PARI) a(n)=if(n>2, precprime(2*n), 2) \\ Charles R Greathouse IV, Nov 17 2015


CROSSREFS

Cf. A000108, A006530, A020482, A028334, A060265, A060308, A152765.
Sequence in context: A145378 A069887 A254340 * A093413 A004099 A084959
Adjacent sequences: A120300 A120301 A120302 * A120304 A120305 A120306


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Jul 13 2006


STATUS

approved



