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A000989 3-adic valuation of C(2n, n): largest k such that 3^k divides C(2n,n). 3
0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 3, 2, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 3, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3, 4, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

a(n) = 0 if and only if n is in A005836. - Charles R Greathouse IV, May 19 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Michael Gilleland, Some Self-Similar Integer Sequences

FORMULA

a(n) = sum(k>=0, floor(2*n/3^k))-2*sum(k>=0, floor(n/3^k)). - Benoit Cloitre, Aug 26 2003

a(n) = A007949(A000984(n)). - Reinhard Zumkeller, Nov 19 2015

MATHEMATICA

p=3; Array[ If[ Mod[ bi=Binomial[ 2#, # ], p ]==0, Select[ FactorInteger[ bi ], Function[ q, q[ [ 1 ] ]==p ], 1 ][ [ 1, 2 ] ], 0 ]&, 27*3, 0 ]

Table[ IntegerExponent[ Binomial[2 n, n], 3], {n, 0, 100}] (* Jean-Fran├žois Alcover, Feb 15 2016 *)

PROG

(PARI) a(n)=valuation(binomial(2*n, n), 3)

(PARI) a(n)=my(N=2*n, s); while(N\=3, s+=N); while(n\=3, s-=2*n); s \\ Charles R Greathouse IV, May 19 2013

(Haskell)

a000989 = a007949 . a000984  -- Reinhard Zumkeller, Nov 19 2015

CROSSREFS

Cf. A007949, A000984.

Sequence in context: A062979 A114781 A083890 * A132401 A104273 A051778

Adjacent sequences:  A000986 A000987 A000988 * A000990 A000991 A000992

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, R. K. Guy

STATUS

approved

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Last modified June 1 01:18 EDT 2016. Contains 273548 sequences.