A262070 a(n) = ceiling( log_3( binomial(n,2) ) ).

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

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) 93-101 eq. (3).

Anping Li, On the conjecture at two counterfeit coins, Discr. Math. 133 (1-3) (1994) 301-306

Wen An Liu, Qi Min Zhang, Zan Kan Nie, Optimal search procedure on coin-weighing problem, J. Statl. Plan. Inf. 136 (2006) 4419-4435.

R. Tosic, Two counterfeit coins, Discr. Math. 46 (3) (1993) 295-298, 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 Hellström, 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 A351115 A085423

Adjacent sequences: A262067 A262068 A262069 * A262071 A262072 A262073

Keyword

nonn,easy

Author

R. J. Mathar, Sep 10 2015

Status

approved