A selection using binary digits

[A recent private mail from Giorgos Kalogeropoulos]

(...)
This sequence transforms every integer n using a simple rule:
Let's say we want to transform n = 14862 which in base 2 is 11101000001110
We write down the digits of both bases:
base 10  ->  1, 4, 8, 6, 2
base  2  ->  1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0
We now remove the extra trailing digits in base 2 (blue italic) and we only keep the first k digits (where k is the number of digits of n in base 10):
base 10  ->  1, 4, 8, 6, 2
base  2  ->  1, 1, 1, 0, 1
Now, from the original digits of n we only keep those who have the digit "1" underneath them.
In this case we keep 1,4,8,2
So, 14862 becomes 1482.
That's it!
The first 100 terms of this sequence are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 12, 13, 14, 15, 1, 1, 1, 1, 2, 2, 2, 2, 24, 25, 26, 27, 28, 29, 30, 31, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 96, 97, 98, 99, 10...

The first 100000 terms produce a Kandinsky-like plot :)
We can also produce a second sequence by accepting the last digits of base 2 and discarding the first ones like this:
base 10  ->                             1, 4, 8, 6, 2
base  2  ->  1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0
In this case we have 
base 10  ->   1, 4, 8, 6, 2
base  2  ->   0, 1, 1, 1, 0
We keep the digits 4,8,6 and the number 14862 becomes 486

The first 100 terms of the second sequence are:
1, 0, 3, 0, 5, 0, 7, 0, 9, 1, 11, 0, 3, 1, 15, 0, 7, 1, 19, 0, 1, 2, 23, 0, 5, 2, 27, 0, 9, 3, 31, 0, 3, 3, 35, 0, 7, 3, 39, 0, 1, 4, 43, 0, 5, 4, 47, 0, 9, 5, 51, 0, 3, 5, 55, 0, 7, 5, 59, 0, 1, 6, 63, 0, 5, 6, 67, 0, 9, 7, 71, 0, 3, 7, 75, 0, 7, 7, 79, 0, 1, 8, 83, 0, 5, 8, 87, 0, 9, 9, 91, 0, 3, 9, 95, 0, 7, 9, 99, 1

Here are the first 100000 terms plotted:
(I like the fact that although we have pretty much the same rule the graph is now highly structured!)
Best,
GK.
____________________
Indeed, Giorgos, to compare both graphs is a delight, bravo!
(Dall-e creation)



 










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