get equation of number sequence

hi. for example i have a set of numbers (4 columns and 2 of them never changes). how can i get equation so to calculate future numbers ( like knowing 3 of number getting 4th)?

[Torsten]

The easiest way is to find out how these number sets were generated.

Best wishes

Torsten.

Answer 1

[Jan]

19.

According to Carl E. Linderholm’s great classic Mathematics Made Difficult, the next term is always 19, whatever the sequence: 1, 2, 3, 4, 5—19 and 1, 2, 4, 8, 16, 32—19. Even 2, 3, 5, 7, 11, 13, 17—19.

Any other value fits also. You can always find a Laplace interpolation with an arbitrary following parameter, so choosing the same number is the most efficient solution. Choosing your favorite number might cause insights into your mind, so better use the 19.

[Stephen23]

I suspect that there are a few (possibly infinite) sequences where this does not work, such as

19, 19, 19, 19, 19, 19, 19, ... ???

and

13, 14, 15, 16, 17, 18, ... ???

"Choosing your favorite number might cause insights into your mind" creates a paradox: surely the choice of not choosing your favorite number (and selecting 19 by default) also causes insights...