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Search: id:A120274
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| A120274 |
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Largest prime factor of the odd Catalan number A038003(n). |
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+0
2
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| 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; listen)
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OFFSET
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2,1
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COMMENT
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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 (rgwv(AT)rgwv.com), May 11 2007
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FORMULA
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Equals greatest prime less than 2^n-2. - Robert G. Wilson v (rgwv(AT)rgwv.com), May 11 2007
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EXAMPLE
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a(2) = 5 because A038003[2] = 5.
a(3) = 13 because A038003[3] = 429 = 3*11*13.
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MATHEMATICA
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(* 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 (rgwv(AT)rgwv.com), 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 (rgwv(AT)rgwv.com), May 11 2007
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CROSSREFS
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Cf. A038003, A000108, A014234, A028367.
Sequence in context: A020576 A093810 A093817 this_sequence A036982 A029580 A113914
Adjacent sequences: A120271 A120272 A120273 this_sequence A120275 A120276 A120277
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 04 2006, Jul 13 2006, Jul 26 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 11 2007
Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 15 2007
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