find formula of function

45 Views Asked by At

4 ->2

5 ->2

6 ->2

8 ->4

9 ->4

10->4

12->6

13->6

14->6 ....

then let k be (2,3,4,6,...) and n be (4,5,6,8,9,10,12,13,14...)

then I have

$2k≤n≤2k+2$

$2k-1≤n-1≤2k+1$

$k-1/2≤(n-1)/2≤k+1/2$

$k≤(n-1)/2+1/2≤k+1$

but I cannot apply floor function or ceiling function.

If I have that

$2k≤n<2k+3$

$2k-3/2≤n-3/2<2k+3/2$

$k-3/4≤n/2-3/4<k+3/4$

$k≤n/2<k+3/2$

but I still cannot apply floor function or ceiling function.

Doesn't the formula exist?

1

There are 1 best solutions below

0
On BEST ANSWER

$$n\le2k\lt n+4$$

$$\dfrac n4\le \dfrac k2\lt \dfrac n4+1$$

$$\dfrac k2=\left\lfloor \dfrac n4 \right\rfloor$$

$$k=2\left\lfloor \dfrac n4\right\rfloor$$