# Reverse formula for arithmetic progression

Need formula for:

f(x) => y

where x and y are:

0..4 => 1

5..14 => 2

15..29 => 3

30..49 => 4

etc.

i also need the opposite:

f(a) => b,c

where a,b and c are:

1 => 0,5

2 => 5,10

3 => 15,15

4 => 30,20

I'm stumped. Thanks in advance! I'm currently pursuing getting the largest consecutive numbers which satisfy n * (n+1) / 2 by getting a sqrt on the sum (after dividing by 5) since the sums are scaled x5.

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