A096198 Triangle read by rows: T(m,n)=A029837(m)+A029837(n), where (m,n)=(1,1); (2,1), (1,2); (3,1), (2,2), (1,3); ...

0, 1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 4, 3, 3, 3, 4, 4, 4, 4, 3, 3, 4, 5, 4, 5, 4, 3, 3, 4, 5, 5, 5, 5, 4, 3, 4, 4, 5, 5, 6, 5, 5, 4, 4, 4, 5, 5, 5, 6, 6, 5, 5, 5, 4, 4, 5, 6, 5, 6, 6, 6, 5, 6, 5, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 5, 4, 4, 5, 6, 6, 7, 6, 6, 6, 7, 6, 6, 5, 4, 4, 5, 6, 6, 7, 7, 6, 6, 7, 7, 6, 6, 5, 4

Offset

1,4

Comments

A029837(n) is the smallest k such that 2^k>=n. T(m,n) is the solution to the following simple problem. What is the minimum number of cuts needed to divide a sheet of paper whose sides are in the ratio m:n into mn square pieces of equal size? (A single cut means either cutting one rectangle into two smaller rectangles or placing two or more sheets on top of one another and cutting through the lot in one go.)

Links

Table of n, a(n) for n=1..105.

Example

Array begins
0
1 1
2 2 2
2 3 3 2
3 3 4 3 3

Mathematica

t[n_, k_] := Ceiling[Log[2, k]] + Ceiling[Log[2, n-k+1]]; Table[t[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Feb 24 2015 *)

Crossrefs

Cf. A029837.

Sequence in context: A023516 A156607 A093450 * A103183 A335898 A143901

Adjacent sequences: A096195 A096196 A096197 * A096199 A096200 A096201

Keyword

easy,nonn,tabl

Author

Paul Boddington, Jul 26 2004

Status

approved