My apologies if this was asked here before.
My friend and I want to do this:
Suppose that we have some real number $a. a_1 a_2...a_n...$ where $a_i$ are digits in the set $\{1,2,3,4,5,6,7,8,9,0\}$ (so we are in the world of decimal expansion).
We can discard non-decimal-part digit and turn it into 0 so we have now number $0. a_1 a_2...a_n...$
From this number we want to make a sequence of natural numbers that is defined in this way:
$a_1,a_1 a_2,a_1 a_2 a_3, a_1 a_2 a_3 a_4...$
That is, we want from decimal part of a real number to take first digit as one-digit natural number which is first in the new sequence, first two as two-digit natural number which is second in the new sequence, and so on...
As an example, suppose that we have real number $0.123456345436...$. We want that Mathematica take that real number as an input and that gives us output (with commas, of course):
$1,12,123,1234,12345,123456,1234563,12345634...$
How to do that in Mathematica?