A064099 a(n) = ceiling(log(3 + 2*n)/log(3)).

1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 0

Author

Eugene McDonnell (EEMcD(AT)AOL.com), Sep 16 2001

Keywords

• nice
• easy
• nonn

Comments

Minimal number of weighings to detect a heavier or lighter counterfeit coin among n coins.

The relation is given via the inverse (A003462) and the comments in A029858. - R. J. Mathar, Sep 10 2015

Examples

			It would be nice to have some examples showing how the sequence is related to the coin problem! - _N. J. A. Sloane_, Jun 25 2002
		

References

• J. G. Mauldon, Strong solutions for the counterfeit coin problem. IBM Research Report RC 7476 (#31437) 9/15/78, IBM Thomas J. Watson Research Center, P. O. Box 218, Yorktown Heights, N. Y. 10598

Links

• Harry J. Smith, Table of n, a(n) for n=0,...,1000
• Gary Darby, The Counterfeit Coin
• Gary Darby, Martin Gardner and The Counterfeit Coin Problem
• M. Gardner, logic/weighing/balance.s on the counterfeit coin weighing.

Crossrefs

Cf. A003462 ((3^n-1)/2, the inverse).

Programs

Maple

A064099 := n->ceil(evalf(log(3+2*n)/log(3)));

Mathematica

Table[Ceiling[Log[3,3+2n]],{n,0,100}] (* Harvey P. Dale, Oct 26 2015 *)

PARI

{ for (n=0, 1000, write("b064099.txt", n, " ", ceil(log(3 + 2*n)/log(3))) ) } \\ Harry J. Smith, Sep 07 2009

Formula

a(n) = A134021(n+1). - Reinhard Zumkeller, Oct 19 2007