NestWhileList

NestWhileList[f, expr, test] generates a list of results from applying f repeatedly until test fails.

NestWhileList[f, expr, test, m, max] applies f at most max times.

Examples

Divide by 2 while even:

NestWhileList[#/2 &, 64, EvenQ]
(* {64, 32, 16, 8, 4, 2, 1} *)

Collatz sequence:

NestWhileList[If[EvenQ[#], #/2, 3# + 1] &, 7, # != 1 &]
(* {7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1} *)

Please visit the official Wolfram Language Reference for more details.