NestWhile

Applies a function repeatedly while a test on the current value holds.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageNestWhile✓↗

NestWhile(f, x, test)Applies $f$ to $x$ repeatedly while $test$ of the CURRENT value reads $True$, and returns the first value where it doesn't.

NestWhile(f, x, test, m)$test$ is called on the last $m$ values as $m$ separate arguments, instead of the bare current value.

NestWhile(f, x, test, m, max)Additionally caps the number of $f$-applications at $max$.

Typed signatures

Type	Package	Applies
(any, any, any, integer?, integer?) -> any	combinatorics	always

Domain: Collections

Details

• With $m > 1$, the test waits until $m$ values exist, so $f$ runs $m - 1$ times before the first test.
• Capped at 4096 applications of $f$ regardless of $max$ — see While.

Examples

Basic #

halve while even, stopping at the first odd value

live ↗

In$\mathrm{NestWhile}(\operatorname{\_1}↦\frac{\operatorname{\_1}}{2}, 96, \operatorname{\_1}↦\operatorname{\_1}\bmod2=0)$Out$3$

Divides by $2$ while even, leaving the odd part: $123456 = 2^6\cdot1929$

live ↗

In$\mathrm{NestWhile}(\operatorname{\_1}↦\frac{\operatorname{\_1}}{2}, 123\,456, \mathrm{IsEven})$Out$1\,929$

Iterated logs of $100$ until the value turns negative; stays symbolic

live ↗

In$\mathrm{NestWhile}(\ln, 100, \operatorname{\_1}↦\operatorname{\_1}\gt0)$Out$\ln(\ln(\ln(2\ln(10))))$

Scope #

With a lookback of one and a cap of four steps, it stops early

live ↗

In$\mathrm{NestWhile}(\operatorname{\_1}↦\frac{\operatorname{\_1}}{2}, 123\,456, \mathrm{IsEven}, 1, 4)$Out$7\,716$

live ↗

In$\mathrm{NestWhile}(\operatorname{\_1}↦\lfloor\frac{\operatorname{\_1}}{2}\rfloor, 10, \mathrm{UnsameQ}, 2)$Out$5$

Applications #

The first prime above $888$ is $907$

live ↗

In$\mathrm{NestWhile}(\operatorname{\_1}↦\operatorname{\_1}+1, 888, \operatorname{\_1}↦¬\mathrm{IsPrime}(\operatorname{\_1}))$Out$907$

Smallest $n$ with $F_n > 10^6$ is $31$

live ↗

In$\mathrm{NestWhile}(\operatorname{\_1}↦\operatorname{\_1}+1, 1, \operatorname{\_1}↦\mathrm{Fibonacci}(\operatorname{\_1})≤10^6)$Out$31$

live ↗

In$\mathrm{NestWhile}(\operatorname{\_1}↦\operatorname{\_1}+1, 888, (\operatorname{\_1}, \operatorname{\_3})↦¬\mathrm{IsPrime}(\operatorname{\_1})∨¬\mathrm{IsPrime}(\operatorname{\_3}), 3)$Out$1\,021$

Properties #

Halves with floor until it hits $0$

live ↗

In$\mathrm{NestWhile}(\operatorname{\_1}↦\lfloor\frac{\operatorname{\_1}}{2}\rfloor, 10, \operatorname{\_1}↦\operatorname{\_1}\gt0)$Out$0$

live ↗

In$\mathrm{NestWhile}(\operatorname{\_1}↦\lfloor\frac{\operatorname{\_1}}{2}\rfloor, 10, \mathrm{UnsameQ}, 4)$Out$1$

live ↗

In$\mathrm{NestWhile}(\operatorname{\_1}↦11\mathrm{PrimePi}(\operatorname{\_1})+1, 2, \mathrm{UnsameQ}, 2)$Out$12$

About

Examples	11
Checked against	Wolfram Language 11 agree
Crosswalk	Wolfram Language

See also: NestWhileList, While, FixedPointList