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

0,2

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

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.

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A343607 A269024 A244160 * A134021 A330558 A237657

Adjacent sequences: A064096 A064097 A064098 * A064100 A064101 A064102

Keyword

nice,easy,nonn

Author

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

Status

approved