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

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





[SIZE="5"]5.2/3.999999999999999^1.618033988749(27+(sqrt(2^2-1))^3)+2^[COLOR="Red"]2[/COLOR]-1[/SIZE]

[QUOTE=ONeil;485495]I was fulling around with the golden ratio and some other numbers at
[URL="https://keisan.casio.com/calculator"]https://keisan.casio.com/calculator[/URL] and I produced this algorithm. The input is in red. It will find mersenne numbers





[SIZE="5"]5.2/3.999999999999999^1.618033988749(27+(sqrt(2^2-1))^3)+2^[COLOR="Red"]2[/COLOR]-1[/SIZE][/QUOTE]I tried with changing the red number to 7 and got 144.768623663...

What did I do wrong?

[QUOTE=retina;485496]I tried with changing the red number to 7 and got 144.768623663...

What did I do wrong?[/QUOTE]

In Wolfram's syntax:
[CODE]
5.2/4^((Sqrt[5]+1)/2*(27+(Sqrt[2^2-1])^3))+2^2-1
[/CODE]
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.

[QUOTE=retina;485496]I tried with changing the red number to 7 and got 144.768623663...

What did I do wrong?[/QUOTE]
did you use it at casio?

it works perfectly for me

[QUOTE=R. Gerbicz;485497]In Wolfram's syntax:
[CODE]
5.2/4^((Sqrt[5]+1)/2*(27+(Sqrt[2^2-1])^3))+2^2-1
[/CODE]
it is pretty close to 3, but isn't exactly 3[/QUOTE]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

[QUOTE=R. Gerbicz;485497]In Wolfram's syntax:
[CODE]
5.2/4^((Sqrt[5]+1)/2*(27+(Sqrt[2^2-1])^3))+2^2-1
[/CODE]
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.[/QUOTE]

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

[QUOTE=ONeil;485499]did you use it at casio?

it works perfectly for me[/QUOTE]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.

[QUOTE=retina;485504]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.[/QUOTE]

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

[QUOTE=ONeil;485505]I just find it to be fascinating that the golden ratio computes this along with the algo.[/QUOTE]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.

[QUOTE=retina;485506]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.[/QUOTE]


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

[QUOTE=ONeil;485508]Still its interesting because you can edit to get other outputs.[/QUOTE]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.[QUOTE=ONeil;485508]Retina what is the difference between an algorithm and a formula?[/QUOTE]:google:

[QUOTE=retina;485509]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.:google:[/QUOTE]
I guess you don't the answer so later dude

[QUOTE=ONeil;485510]I guess you don't the answer so later dude[/QUOTE]

He just wants you to use google to find it yourself.

[QUOTE] for·mu·la
ˈfôrmyələ/
noun
1.
a mathematical relationship or rule expressed in symbols. [/QUOTE]

[QUOTE] al·go·rithm
ˈalɡəˌriT͟Həm/
noun
noun: algorithm; plural noun: algorithms
a process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer.
"a basic algorithm for division" [/QUOTE]