simple number series | 易学教程

问题

This is a simple number series question, I have numbers in series like 2,4,8,16,32,64,128,256 these numbers are formed by 2,2(square),2(cube) and so on.

Now if I add 2+4+8 = 14. 14 will get only by the addition 2,4 and 8. so i have 14in my hand now, By some logic i need to get the values which are helped to get 14

Example:

2+4+8 = 14
14(some logic) = 2,4,8.

回答1:

This is an easy one:

2+4+8=14 ... 14+2=16
2+4+8+16=30 ... 30+2=32
2+4+8+16+32=62 ... 62+2=64

So you just need to add 2 to your sum, then calculate ld (binary logarithm), and then subtract 1. This gives you the number of elements of your sequence you need to add up.

e.g. in PHP:

$target=14;
$count=log($target+2)/log(2)-1;
echo $count;

gives 3, so you have to add the first 3 elements of your sequence to get 14.

回答2:

Check the following C# code:

x = 14; // In your case
indices = new List<int>();
for (var i = 31; i >= i; i--)
{
   var pow = Math.Pow(2, i);
   if x - pow >= 0)
   {
       indices.Add(pow);
       x -= pow;
   }
}

indices.Reverse();

回答3:

assuming C:

unsigned int a = 14;
while( a>>=1)
{
printf("%d ", a+1);
}

回答4:

if this is programming, something like this would suffice:

int myval = 14;
int maxval = 256;
string elements = "";
for (int i = 1; i <= maxval; i*=2)
{
if ((myval & i) != 0)
elements += "," + i.ToString();
}

回答5:

Use congruency module 2-powers: 14 mod 2 = 0, 14 mod 4 = 2, 14 mod 8 = 6, 14 mod 16 = 14, 14 mod 32 = 14... The differences of this sequence are the numbers you look for 2 - 0 = 2, 6 - 2 = 4, 14 - 6 = 8, 14 - 14 = 0, ...

It's called the p-adic representation and is formally a bit more difficult to explain, but I hope this gives you an idea for an algorithm.

来源：https://stackoverflow.com/questions/9291308/simple-number-series

标签

numbers

series