How can I transform this sequence: "0-1-2-5-15-50" into this one: "0-1-2-3-4-5"?

[RodesRodes]

How can I transform this sequence: "0-1-2-5-15-50" into this one: "0-1-2-3-4-5"?
The main goal is to know for example, if I put a new number on one of those sequences, what number would it represent in he other one?
For example, if we introduce an 1,25 in the first sequence, what number would it represent in the second sequence?

 

[Deleted member 4993]

How can I transform this sequence: "0-1-2-5-15-50" into this one: "0-1-2-3-4-5"?
The main goal is to know for example, if I put a new number on one of those sequences, what number would it represent in he other one?
For example, if we introduce an 1,25 in the first sequence, what number would it represent in the second sequence?

If you do NOT want the exact numbers (close-enough will do) - then use Ms_excel and fit line y = A* e^(B*x).

 

[Dr.Peterson]

If you do NOT want the exact numbers (close-enough will do) - then use Ms_excel and fit line y = A* e^(B*x).

Exponential and logarithmic formulas won't work with zeros.

The reverse direction can be done as a polynomial (y = 0.0833x⁵ - 0.7083x⁴ + 2.5x³ - 3.7917x² + 2.9167x), but that can't be easily inverted. (You could do it using other technology, e.g. Desmos.)

Of course, we don't really know how the numbers are related, so a polynomial may not be appropriate either.

How can I transform this sequence: "0-1-2-5-15-50" into this one: "0-1-2-3-4-5"?
The main goal is to know for example, if I put a new number on one of those sequences, what number would it represent in he other one?
For example, if we introduce an 1,25 in the first sequence, what number would it represent in the second sequence?

The big question is, where did those numbers come from? With context, it may be possible to figure out the real relationship.

 

[Deleted member 4993]

Exponential and logarithmic formulas won't work with zeros.

Yes - I dumped the point (0,0) - and excel fitted a curve with R² ~ 0.99

 

[RodesRodes]

T

Exponential and logarithmic formulas won't work with zeros.

The zeros don't matter
I have a movie and the audio separated, the movie is 126 long and the audio is distorted, it is 136 min long BUT the delay is exponential, to give an example the first phrase is on time, the second is delayed one second but the third is delayed 3 and so on, I hope I made myself clear.