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NestWhile
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NestWhile

NestWhile[f,expr,test]

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

NestWhile[f,expr,test,m]

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

NestWhile[f,expr,test,All]

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

NestWhile[f,expr,test,m,max]

applies f at most max times.

NestWhile[f,expr,test,m,max,n]

applies f an extra n times.

NestWhile[f,expr,test,m,max,-n]

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

Details

  • 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.

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

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

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-y1
Out[1]=1

Iterate taking logarithms until the result is no longer positive:

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-wba
Out[1]=1

Scope  (5)Survey of the scope of standard use cases

Compare the last two values generated:

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-lgmldb
Out[1]=1

Always compare all values generated:

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-k60s56
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-t2u457
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-zhom6v
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-8krxt6
Out[1]=1

Generalizations & Extensions  (2)Generalized and extended use cases

Continue until the result is no longer greater than 1:

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-0bqu8h
Out[1]=1

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

In[2]:=2
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https://wolfram.com/xid/0cg5nevbq-8xuhnc
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-ev4bxa
Out[1]=1

Applications  (3)Sample problems that can be solved with this function

Find the next prime after 888:

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-uvq
Out[1]=1

Find the next twin prime after 888:

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-ga
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-qt2
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cg5nevbq-mto
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0cg5nevbq-cq2
Out[3]=3

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

In[4]:=4
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https://wolfram.com/xid/0cg5nevbq-e060as
Out[4]=4

Properties & Relations  (5)Properties of the function, and connections to other functions

These two forms are equivalent:

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-pvvciq
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cg5nevbq-3jni4a
Out[2]=2

NestWhile returns if the condition returns anything other then True:

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-te7kib
Out[1]=1

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

In[2]:=2
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https://wolfram.com/xid/0cg5nevbq-qlkpr9
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-q9ips1
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cg5nevbq-qmo6dq
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0cg5nevbq-pzsdgx
Out[1]=1

NestWhile can be expressed in terms of a While loop:

In[1]:=1
✖
https://wolfram.com/xid/0cg5nevbq-fm75fz
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0cg5nevbq-o8ed7y
Out[2]=2
Wolfram Research (1999), NestWhile, Wolfram Language function, https://reference.wolfram.com/language/ref/NestWhile.html.
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Wolfram Research (1999), NestWhile, Wolfram Language function, https://reference.wolfram.com/language/ref/NestWhile.html.

Text

Wolfram Research (1999), NestWhile, Wolfram Language function, https://reference.wolfram.com/language/ref/NestWhile.html.

✖
Wolfram Research (1999), NestWhile, Wolfram Language function, https://reference.wolfram.com/language/ref/NestWhile.html.

CMS

Wolfram Language. 1999. "NestWhile." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NestWhile.html.

✖
Wolfram Language. 1999. "NestWhile." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NestWhile.html.

APA

Wolfram Language. (1999). NestWhile. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NestWhile.html

✖
Wolfram Language. (1999). NestWhile. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NestWhile.html

BibTeX

@misc{reference.wolfram_2025_nestwhile, author="Wolfram Research", title="{NestWhile}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/NestWhile.html}", note=[Accessed: 06-June-2025 ]}

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@misc{reference.wolfram_2025_nestwhile, author="Wolfram Research", title="{NestWhile}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/NestWhile.html}", note=[Accessed: 06-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_nestwhile, organization={Wolfram Research}, title={NestWhile}, year={1999}, url={https://reference.wolfram.com/language/ref/NestWhile.html}, note=[Accessed: 06-June-2025 ]}

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@online{reference.wolfram_2025_nestwhile, organization={Wolfram Research}, title={NestWhile}, year={1999}, url={https://reference.wolfram.com/language/ref/NestWhile.html}, note=[Accessed: 06-June-2025 ]}