OFFSET
2,1
COMMENTS
For n=6 a(n) differs from the largest prime factor of (2*(2^n-1))! = A028367[n].
A038003[n] = binomial(2^(n+1)-2, 2^n-1)/(2^n).
The numbers of distinct prime factors of the odd Catalan numbers A038003(n): 3, 6, 11, 20, 36, 64, 117, 209, 381, 699, 1291, 2387, 4445, 8317, 15645, 29494, ..., . - Robert G. Wilson v, May 11 2007
LINKS
Harvey P. Dale, Table of n, a(n) for n = 2..1000
FORMULA
Equals greatest prime less than 2^n-2. - Robert G. Wilson v, May 11 2007
MATHEMATICA
(* first do *) Needs["DiscreteMath`CombinatorialFunctions`"] (* then *) f[n_] := FactorInteger[CatalanNumber[2^n - 1]][[ -1, 1]]; lst = {}; Do[ Append[lst, f@n], {n, 2, 20}]; lst (* Or *) (* Robert G. Wilson v, May 11 2007 *)
PrevPrim[n_] := Block[{k = n - 1}, While[ ! PrimeQ@k, k-- ]; k]; Table[ PrevPrim[2^n - 2], {n, 3, 32}] (* Robert G. Wilson v, May 11 2007 *)
Table[NextPrime[2^n-2, -1], {n, 3, 50}] (* Harvey P. Dale, Apr 22 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Jul 04 2006, Jul 13 2006, Jul 26 2006
EXTENSIONS
More terms from Robert G. Wilson v, May 11 2007
Edited by N. J. A. Sloane, Oct 15 2007
STATUS
approved