starts with expr, then repeatedly applies f until applying test to the result no longer yields True.


supplies the most recent m results as arguments for test at each step.


supplies all results so far as arguments for test at each step.


applies f at most max times.


applies f an extra n times.


returns the result found when f had been applied n fewer times.


  • NestWhile[f,expr,test] returns the first expression f[f[ f[expr]]] to which applying test does not yield True.
  • If test[expr] does not yield True, NestWhile[f,expr,test] returns expr. »
  • NestWhile[f,expr,test,m] at each step evaluates test[res1,res2,,resm]. It does not put the results resi in a list. »
  • The resi are given in the order they are generated, with the most recent coming last.
  • NestWhile[f,expr,test,m] does not start applying test until at least m results have been generated.
  • NestWhile[f,expr,test,{mmin,m}] does not start applying test until at least mmin results have been generated. At each step it then supplies as arguments to test as many recent results as possible, up to a maximum of m. »
  • NestWhile[f,expr,test,m] is equivalent to NestWhile[f,expr,test,{m,m}]. »
  • NestWhile[f,expr,UnsameQ,2] is equivalent to FixedPoint[f,expr]. »
  • NestWhile[f,expr,test,All] is equivalent to NestWhile[f,expr,test,{1,Infinity}]. »
  • NestWhile[f,expr,UnsameQ,All] goes on applying f until the same result first appears more than once.
  • NestWhile[f,expr,test,m,max,n] applies f an additional n times after test fails, or max applications have already been performed. »
  • NestWhile[f,expr,test,m,max,-n] is equivalent to Part[NestWhileList[f,expr,test,m,max],-n-1]. »
  • NestWhile[f,expr,test,m,Infinity,-1] returns, if possible, the last expression in the sequence expr, f[expr], f[f[expr]], for which test yields True.


open allclose all

Basic Examples  (2)

Keep dividing by 2 until the result is no longer an even number:

Iterate taking logarithms until the result is no longer positive:

Scope  (5)

Compare the last two values generated:

Always compare all values generated:

Start comparisons after 4 iterations, and compare using the 4 last values:

Start comparisons after 4 iterations, and compare using the 6 last values:

Stop after at most 4 iterations, even if the test is still True:

Generalizations & Extensions  (2)

Continue until the result is no longer greater than 1:

Perform one more step after the condition is no longer True:

Return the last value for which the condition was still True:

Applications  (3)

Find the next prime after 888:

Find the next twin prime after 888:

Find the index of the first Fibonacci number above a million:

Find the index of the last Fibonacci number below a million:

Properties & Relations  (5)

These two forms are equivalent:

NestWhile returns if the condition returns anything other then True:

The outcome of a condition need not be True or False:

FixedPoint always compares the last two values; these two forms are equivalent:

NestWhileList applies the same stopping criteria, but returns all values generated:

NestWhile can be expressed in terms of a While loop:

Introduced in 1999