A sort of Addition/Subtraction version of the distributive property perhaps?
I was looking at a door code, and the pattern was similar to this:
6 9 3 4 7 1
Which I noticed was 6 9 3 (6-2) (9-2) (3-2), and I was wondering if there was a mathematical tool that can generate that other than just subtracting 2 from every number, and when I came up empty, I thought, maybe I can make one?
So, I'm kicking around this idea. A sort of operator maybe? Something like these examples:
(+2) (a, b) = (a+2, b+2)
or
(+2| x, y) (x^2 + y^2 + z^2) = ( (x+2)^2 + (y+2)^2 + z^2)
or even something fancier like
(+2...6) (a, b) = (a+2, b+2, a+3, b+3, a+4, b+4, a+5, b+5, a+6, b+6)
Is this type of thing already covered somehow? I have no illusions of this being extremely useful or whatever, or it would already exist. But I came across it in real life, so there's at least some utility I suppose. Thoughts? Delete my account?