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

2,1

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

Example

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

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

Cf. A038003, A000108, A014234, A028367.

Sequence in context: A020576 A093810 A093817 * A036982 A029580 A344920

Adjacent sequences: A120271 A120272 A120273 * A120275 A120276 A120277

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