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 A120274 Largest prime factor of the odd Catalan number A038003(n). 6
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 28 08:48 EST 2022. Contains 358407 sequences. (Running on oeis4.)