BUILT-IN MATHEMATICA SYMBOL

NestWhileList

generates a list of the results of applying f repeatedly, starting with expr, and continuing until applying test to the result no longer yields True.

NestWhileList

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

NestWhileList[f, expr, test, All]
supplies all results so far as arguments for test at each step.

NestWhileList

applies f at most max times.

MORE INFORMATION

The last element of the list returned by NestWhileList is always an expression to which applying test does not yield True.

NestWhileList at each step evaluates . It does not put the results in a list.

The are given in the order they are generated, with the most recent coming last.

NestWhileList does not start applying test until at least m results have been generated. »

NestWhileList does not start applying test until at least 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. »

NestWhileList is equivalent to NestWhileList. »

NestWhileList[f, expr, UnsameQ, 2] is equivalent to FixedPointList. »

NestWhileList[f, expr, test, All] is equivalent to NestWhileList[f, expr, test, {1, Infinity}]. »

NestWhileList[f, expr, UnsameQ, All] goes on applying f until the same result first appears more than once.

NestWhileList applies f an extra n times, appending the results to the list generated. »

NestWhileList drops the last n elements from the list generated. »

EXAMPLES

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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:

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

In[1]:=

Out[1]=

Iterate taking logarithms until the result is no longer positive:

In[1]:=

Out[1]=

Scope (4)

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

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

Always compare all values generated:

Stop after at most 4 steps, even if the condition is still True:

Generalizations & Extensions (1)

Continue until the result is no longer greater than 1:

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

Drop the last value generated (for which the test was no longer True):

Applications (5)

Find successive integers until a prime is reached:

Find the multiplicative order of 2 modulo 19:

Use MultiplicativeOrder to compute directly:

Find the orbit of

under the mapping

:

Keep applying iterations in the

problem until the results repeat:

Exclude the first repeating element from the output:

Apply Newton iterations for

until successive results are within 0.001.

Properties & Relations (3)

These two forms are equivalent:

NestWhileList returns all intermediate values of NestWhile:

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

Neat Examples (2)

Find the digits of a number:

Distance of two vertices in a graph:

A plot of the graph: