Can You Derive a Mathematical Formula from This Data Pattern?

[rishid]

Need to analyze the pattern and create a formula if possible out of the data below. Inputting the first column and outputting the second.
1 1
2 1
3 3
4 1
5 3
6 5
7 7
8 1
9 3
10 5
11 7
12 9
13 11
14 13
15 15
16 1

Only thing I got that is on powers of 2, it should be 1.

If you got any ideas, throw them at me.

Thanks,

RishiD

 

[chroot]

Looks like it's just going through the odd integers, resetting to one on powers of two.

- Warren

 

[matt grime]

Try writing out i rows, starting a new row each time you come across 1. the 'answer' should jump out at you (i'm not sure yo'ure even looking for an answer, to be honest, and what "should be 1").

 

[richJ]

Hello Rishid,
I have the solution to your problem you posted on Oct. 25, 2004.

The formula is: x = 2 i + 1 - (2 ^ (int(log2(i)) + 1)

where i is the integer and x is the result,
log2(n) is the log (base 2) of n,
and int(n) is the integer value of n.

The table illustrates the calcs. (I used periods to line up the values because the message formatting automatically removes extraneous spaces. Also I was forced to use variables to represent each step for the same formatting reason). Specifically,

a = 2i + 1
b= int(log2(i))
c= int(log2(i)) + 1
d = 2^(int(log2(i))+1)
and finally the result you're trying to generate: x = a - d

i...a...b...c...d...x
1...3...0...1...2...1
2...5...1...2...4...1
3...7...1...2...4...3
4...9...2...3...8...1
5...11...2...3...8...3
6...13...2...3...8...5
7...15...2...3...8...7
...
16...33...4...5...32...1

I hope this helps.
RichJ

 

[CellCoree]

Hello RishiD,

Thank you for reaching out with your question. It appears that the second column is following a pattern where the value increases by 2 for every odd number and resets to 1 for every power of 2. This can be represented by the formula:

f(x) = (x-1) mod 2 + 2*((x-1) mod 4) + 1

Where x is the input number and f(x) is the output value. The "mod" function represents the remainder after division. This formula takes into account the increasing pattern for odd numbers and the reset for powers of 2.

I hope this helps you in analyzing the data and creating a formula. Best of luck in your research!

 

[pmacias]

Dear RishiD,

Thank you for reaching out for help with deriving a formula for the given data. After analyzing the pattern, it seems that the first column represents consecutive numbers starting from 1, while the second column follows a repeating pattern of 1, 3, 5, 7, 9, 11, 13, 15, 1. This pattern repeats every 8 numbers.

To create a formula for this pattern, we can use the modulo operator, which gives the remainder after dividing a number by another number. In this case, we can use the formula: (n % 8) + 1, where n represents the number in the first column.

So, the formula for the second column would be: (n % 8) + 1. This formula will give us the desired output for the given input.

I hope this helps. Let me know if you have any further questions.

Best,