Is there any online resource which can calculate the equation for the curve with given points?

Question

I have several sets of Cartesian coordinates and I am looking for a resource which can generate the formula/equation/function for a curve (or line) which passes through these points.

The first set is:

1,1 - 2,2 - 3,5 - 4,7, - 5,12 - 6,15 - 7,22 - 8,35 - 9,40

All help is greatly appreciated. Thanks.

Answer 1

A search found OEIS sequence A024702 "a(n) = (prime(n)^2 - 1)/24". For your sequence of values $\,(1,1),\,(2,2),\,(3,5),\dots\,$ The formula is a(n) = (prime(n+2)^2-1)/24. The first few values are:

1, 2, 5, 7, 12, 15, 22, 35, 40, 57, 70, 77, 92, 117, 145, 155, 187, 210, 222

You are interested OEIS sequence A000040 "prime numbers" with approximation

a(n) = n log n + n log log n + (n/log n)*(log log n - log n - 2) + O( n (log log n)^2/ (log n)^2).

which is probably what you are looking for. Consult the OEIS entry for more information.