My algorithm mimics 2^P-1 with the golden ratio

[ONeil]

I was messing around with the golden ratio and some other numbers at
https://keisan.casio.com/calculator and I produced this algorithm. The input is in red. It will find mersenne numbers





5.2/3.999999999999999^1.618033988749(27+(sqrt(2^2-1))^3)+2^2-1

[retina]

Originally Posted by ONeil

I was fulling around with the golden ratio and some other numbers at
https://keisan.casio.com/calculator and I produced this algorithm. The input is in red. It will find mersenne numbers





5.2/3.999999999999999^1.618033988749(27+(sqrt(2^2-1))^3)+2^2-1

I tried with changing the red number to 7 and got 144.768623663...

What did I do wrong?

[R. Gerbicz]

Originally Posted by retina

I tried with changing the red number to 7 and got 144.768623663...

What did I do wrong?

In Wolfram's syntax:

5.2/4^((Sqrt[5]+1)/2*(27+(Sqrt[2^2-1])^3))+2^2-1

it is pretty close to 3, but isn't exactly 3, how you found this expression?

Trivial solution: the exponent of 4 is large: ((sqrt(5)+1)/2*(27+(sqrt(2^2-1))^3))=52.09, so the 5.2/4^exponent is very small, the expression's value will be close to 2^2-1=3.

[ONeil]

Originally Posted by retina

I tried with changing the red number to 7 and got 144.768623663...

What did I do wrong?

did you use it at casio?

it works perfectly for me

[retina]

Originally Posted by R. Gerbicz

In Wolfram's syntax:

5.2/4^((Sqrt[5]+1)/2*(27+(Sqrt[2^2-1])^3))+2^2-1

it is pretty close to 3, but isn't exactly 3

Taking off the final 2^2-1 the expression is zero (or very near to it).

5.2/4^((Sqrt[5]+1)/2*(27+(Sqrt[2^2-1])^3)) ~= 0

[ONeil]

Originally Posted by R. Gerbicz

In Wolfram's syntax:

5.2/4^((Sqrt[5]+1)/2*(27+(Sqrt[2^2-1])^3))+2^2-1

it is pretty close to 3, but isn't exactly 3, how you found this expression?

Trivial solution: the exponent of 4 is large: ((sqrt(5)+1)/2*(27+(sqrt(2^2-1))^3))=52.09, so the 5.2/4^exponent is very small, the expression's value will be close to 2^2-1=3.

You have to use the exact algo I sent you to produce exact results.

[retina]

Originally Posted by ONeil

did you use it at casio?

it works perfectly for me

It needed an extra set of brackets:

5.2/3.999999999999999^(1.618033988749(27+(sqrt(2^2-1))^3))+2^2-1 ~= 3

So, quite useless IMO.

[ONeil]

Originally Posted by retina

It needed an extra set of brackets:

5.2/3.999999999999999^(1.618033988749(27+(sqrt(2^2-1))^3))+2^2-1 ~= 3

So, quite useless IMO.

I just find it to be fascinating that the golden ratio computes this along with the algo.

[retina]

Originally Posted by ONeil

I just find it to be fascinating that the golden ratio computes this along with the algo.

All you have done is this:

c + 2^n - 1, where c is ~= 10^-31

So it might as well be:

0 + 2^n - 1, which is just 2^n - 1

ETA: It isn't an "algo", it is a formula.

[ONeil]

Originally Posted by retina

All you have done is this:

c + 2^n - 1, where c is ~= 10^-31

So it might as well be:

0 + 2^n - 1, which is just 2^n - 1

ETA: It isn't an "algo", it is a formula.

Still its interesting because you can edit to get other outputs. Retina what is the difference between an algorithm and a formula?

[retina]

Originally Posted by ONeil

Still its interesting because you can edit to get other outputs.

Not really, it is just 2^n-1, not interesting at all unless you consider the trailing 10^-31 (which your calculator hid from you). You are basically saying that 2^n-1 equals 2^n-1.

Originally Posted by ONeil

Retina what is the difference between an algorithm and a formula?