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A262070
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a(n) = ceiling( log_3( binomial(n,2) ) ).
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0
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0, 1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9
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OFFSET
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2,3
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COMMENTS
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A lower bound on the number of weighings which suffice to determine the counterfeit (heavier) coins in a set of n coins given a balance scale and the information that there are exactly two heavier coins present.
Records occur at n=2, 3, 4, 5, 8, 14, 23, 39, 67, 116, 199, 345, 596,...
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LINKS
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MAPLE
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seq(ceil(log[3](binomial(n, 2))), n=2..120) ;
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MATHEMATICA
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Ceiling[Log[3, Binomial[Range[2, 120], 2]]] (* Harvey P. Dale, Dec 13 2016 *)
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PROG
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(PARI) first(m)=vector(m, i, i++; ceil(log(binomial(i, 2))/log(3))) \\ Anders Hellström, Sep 10 2015
(Magma) [Ceiling(Log(3, Binomial(n, 2))): n in [2..120]]; // Bruno Berselli, Sep 10 2015
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CROSSREFS
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Cf. A080342 (single counterfeit coin).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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