NestWhile

NestWhile[f, expr, test] applies f repeatedly to expr until test[result] is no longer True.

NestWhile[f, expr, test, m] supplies the most recent m results to test.

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

Examples

Divide by 2 while even:

NestWhile[#/2 &, 64, EvenQ]
(* 1 *)

Collatz sequence step:

NestWhile[If[EvenQ[#], #/2, 3# + 1] &, 7, # != 1 &]
(* 1 *)

Please visit the official Wolfram Language Reference for more details.