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A000989
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3-adic valuation of C(2n, n): largest k such that 3^k divides C(2n,n).
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2
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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
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OFFSET
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0,6
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COMMENTS
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a(n) = 0 if and only if n is in A005836. - Charles R Greathouse IV, May 19 2013
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Michael Gilleland, Some Self-Similar Integer Sequences
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FORMULA
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a(n)=sum(k>=0, floor(2*n/3^k))-2*sum(k>=0, floor(n/3^k)) - Benoit Cloitre, Aug 26 2003
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MATHEMATICA
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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 ]
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PROG
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(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
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CROSSREFS
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Sequence in context: A062979 A114781 A083890 * A132401 A104273 A051778
Adjacent sequences: A000986 A000987 A000988 * A000990 A000991 A000992
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KEYWORD
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nonn,easy,changed
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AUTHOR
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N. J. A. Sloane, R. K. Guy
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STATUS
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approved
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