A120274 Largest prime factor of the odd Catalan number A038003(n).

5, 13, 29, 61, 113, 251, 509, 1021, 2039, 4093, 8179, 16381, 32749, 65521, 131063, 262139, 524269, 1048573, 2097143, 4194301, 8388593, 16777213, 33554393, 67108859, 134217689, 268435399, 536870909, 1073741789, 2147483629

Offset: 2

Author

Alexander Adamchuk, Jul 04 2006, Jul 13 2006, Jul 26 2006

Keywords

• nonn

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

Examples

			a(2) = 5 because A038003[2] = 5.
a(3) = 13 because A038003[3] = 429 = 3*11*13.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A038003, A000108, A014234, A028367.

Programs

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 *)

Formula

Equals greatest prime less than 2^n-2. - Robert G. Wilson v, May 11 2007

Extensions

More terms from Robert G. Wilson v, May 11 2007

Edited by N. J. A. Sloane, Oct 15 2007