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NestWhile

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NestWhile[f, expr, test]

applies a function f repeatedly on an expression expr, until applying test on the result no longer yields True.

NestWhile[f, expr, test, m]

supplies the last m results to test (default value: 1).

NestWhile[f, expr, test, All]

supplies all results gained so far to test.

Divide by 2 until the result is no longer an integer:

• • NestWhile[#/2&, 10000, IntegerQ]

Calculate the sum of third powers of the digits of a number until the
same result appears twice:

• • NestWhile[Total[IntegerDigits[#]^3] &, 5, UnsameQ, All]

Print the intermediate results:

• • NestWhile[Total[IntegerDigits[#]^3] &, 5, (Print[{##}]; UnsameQ[##]) &, All]