A101290 Dissipation time for n under the following scheme: set f(0)=n, f(i)=0 for all i<>0, then iterate the evolutionary process by which f(i) is replaced by floor[(f(i-1)+f(i)+f(i+1))/3] for all i, with all calculations done in parallel. a(n) is the minimum number of iterations of this process required to reach f(i)=0 for all i, for n=0,1,2,3,...

0, 1, 1, 3, 3, 3, 5, 5, 5, 7, 7, 7, 7, 7, 7, 9, 9, 9, 11, 11, 11, 11, 11, 11, 12, 12, 12, 14, 14, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 22, 22, 22, 23, 23, 23, 23, 23, 23, 25, 25, 25, 25, 25, 25

Offset

0,4

Links

Table of n, a(n) for n=0..74.

Example

If n=10, the process evolves as follows on [ -3,3], showing that a(10)=7:
Start with: 0,0,0,10,0,0,0
Iteration 1: 0,0,3,3,3,0,0
Iteration 2: 0,1,2,3,2,1,0
Iteration 3: 0,1,2,2,2,1,0
Iteration 4: 0,1,1,2,1,1,0
Iteration 5: 0,0,1,1,1,0,0
Iteration 6: 0,0,0,1,0,0,0
Iteration 7: 0,0,0,0,0,0,0

Crossrefs

Sequence in context: A001650 A130175 A200266 * A080605 A130823 A101435

Adjacent sequences: A101287 A101288 A101289 * A101291 A101292 A101293

Keyword

nonn

Author

John W. Layman, Dec 21 2004

Status

approved