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

Author

Paul Boddington, Jul 26 2004

Keywords

• easy
• nonn
• tabl

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.)

Examples

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

Crossrefs

Cf. A029837.

Programs

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 *)