Transforming list elements using Cases[ ]

Questions
1

Re Mathematica 10.3 under Windows 7.

From the list {1,2,3,4,5} I want to zero in on 1 and 3 and return the list of their squares, i.e., {1,9}.

This is easy enough to do using

Cases[Range@5,1|3]^2.

Noting that this example is a grossly oversimplified instance of something else, I want to do this using a form like

Cases[Range@5, (1|3) :> #^2&]

(this returns an empty list). Can this be done? I’ve looked at the documentation PatternOverview and don’t find an answer (although may have missed it).

Thanks.

2

If you want to map a function to list, then

(#^2) & /@ Cases[Range[5], (1 | 3)]

gives

{1, 9}
3

The correct way of using Cases would be:

Cases[Range@5, (x : (1 | 3)) :> x^2]

Cases doesn’t accept pure function like that. Better is to assign it some “named blank” and then transform that.

4

Bingo! Exactly what I sought. Nassir’s earlier reply was also instructive. Thanks to you both, Nassir and Sander.