NestWhileList

Like NestWhile, but returns every intermediate value along the way.

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

NestWhileList(f, x, test)Every value from

x

up to (and including) the first one where

test

fails — the same stopping rule as NestWhile, collected instead of just the last one.

Typed signatures

Type	Package	Applies
`(any, any, any) -> list<any>`	`combinatorics`	always

Domain: Collections

Details

Examples

Basic #

halve while even, collecting every intermediate value

\mathrm{NestWhileList}(\operatorname{\_1}↦\frac{\operatorname{\_1}}{2}, 96, \operatorname{\_1}↦\operatorname{\_1}\bmod2=0)

Out

\bigl\lbrack96, 48, 24, 12, 6, 3\bigr\rbrack

Shows each halving step, ending at the odd part

\mathrm{NestWhileList}(\operatorname{\_1}↦\frac{\operatorname{\_1}}{2}, 123\,456, \mathrm{IsEven})

Out

\bigl\lbrack123\,456, 61\,728, 30\,864, 15\,432, 7\,716, 3\,858, 1\,929\bigr\rbrack

The orbit keeps going until the last value is negative, kept symbolic

\mathrm{NestWhileList}(\ln, 100, \operatorname{\_1}↦\operatorname{\_1}\gt0)

Out

\bigl\lbrack100, 2\ln(10), \ln(2\ln(10)), \ln(\ln(2\ln(10))), \ln(\ln(\ln(2\ln(10))))\bigr\rbrack

Applications #

A prime gap: no primes from $899$ through $906$ , with $907$ next

\mathrm{NestWhileList}(\operatorname{\_1}↦\operatorname{\_1}+1, 899, \operatorname{\_1}↦¬\mathrm{IsPrime}(\operatorname{\_1}))

Out

\bigl\lbrack899, 900, 901, 902, 903, 904, 905, 906, 907\bigr\rbrack

Powers of $2$ mod $19$ cycle back to $1$ after $18$ steps, so $2$ is a primitive root

\mathrm{NestWhileList}(\operatorname{\_1}↦2\operatorname{\_1}\bmod19, 2, \operatorname{\_1}↦\operatorname{\_1}≠1)

Out

\bigl\lbrack2, 4, 8, 16, 13, 7, 14, 9, 18, 17, 15, 11, 3, 6, 12, 5, 10, 1\bigr\rbrack

About