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%I #14 Mar 06 2024 04:48:36
%S 5,13,29,61,113,251,509,1021,2039,4093,8179,16381,32749,65521,131063,
%T 262139,524269,1048573,2097143,4194301,8388593,16777213,33554393,
%U 67108859,134217689,268435399,536870909,1073741789,2147483629
%N Largest prime factor of the odd Catalan number A038003(n).
%C For n=6 a(n) differs from the largest prime factor of (2*(2^n-1))! = A028367[n].
%C A038003[n] = binomial(2^(n+1)-2, 2^n-1)/(2^n).
%C 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
%H Harvey P. Dale, <a href="/A120274/b120274.txt">Table of n, a(n) for n = 2..1000</a>
%F Equals greatest prime less than 2^n-2. - _Robert G. Wilson v_, May 11 2007
%e a(2) = 5 because A038003[2] = 5.
%e a(3) = 13 because A038003[3] = 429 = 3*11*13.
%t (* 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 *)
%t 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 *)
%t Table[NextPrime[2^n-2,-1],{n,3,50}] (* _Harvey P. Dale_, Apr 22 2018 *)
%Y Cf. A038003, A000108, A014234, A028367.
%K nonn
%O 2,1
%A _Alexander Adamchuk_, Jul 04 2006, Jul 13 2006, Jul 26 2006
%E More terms from _Robert G. Wilson v_, May 11 2007
%E Edited by _N. J. A. Sloane_, Oct 15 2007
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