

A262070


a(n) = ceiling( log_3( binomial(n,2) ) ).


0



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

2,3


COMMENTS

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,...


LINKS

Table of n, a(n) for n=2..120.
Anping Li, Three counterfeit coins problem, J. Comb. Theory A 66 (1994) 93101 eq. (3).
Anping Li, On the conjecture at two counterfeit coins, Discr. Math. 133 (13) (1994) 301306
Wen An Liu, Qi Min Zhang, Zan Kan Nie, Optimal search procedure on coinweighing problem, J. Statl. Plan. Inf. 136 (2006) 44194435.
R. Tosic, Two counterfeit coins, Discr. Math. 46 (3) (1993) 295298, eq. (2).


MAPLE

seq(ceil(log[3](binomial(n, 2))), n=2..120) ;


MATHEMATICA

Ceiling[Log[3, Binomial[Range[2, 120], 2]]] (* Harvey P. Dale, Dec 13 2016 *)


PROG

(PARI) first(m)=vector(m, i, i++; ceil(log(binomial(i, 2))/log(3))) \\ Anders HellstrÃ¶m, Sep 10 2015
(MAGMA) [Ceiling(Log(3, Binomial(n, 2))): n in [2..120]]; // Bruno Berselli, Sep 10 2015


CROSSREFS

Cf. A080342 (single counterfeit coin).
Sequence in context: A335741 A103586 A194847 * A117806 A085423 A260998
Adjacent sequences: A262067 A262068 A262069 * A262071 A262072 A262073


KEYWORD

nonn,easy


AUTHOR

R. J. Mathar, Sep 10 2015


STATUS

approved



