Using NestWhileList to determine smallest prime value in series

Question

I have a function recursively defined as follows:

$a_{n+1}-1=(a_n-1)\times lpf(a_n)$, whe $lpf(x)$ is the least prime factor of $x$.

Now, given an initial value of $a_0$, I would like to find the smallest value of $a_n$ such that $a_n$ is prime.

Here is my attempt at a code, with $a_0=6$.

NestWhileList[((#1 - 1)*FactorInteger[#1][[1, 1]] + 1) &, 6, ! PrimeQ]

However, my code always simply returns the initial value of $a_0$. What am I doing wrong here?

Answer 1

!PrimeQ is not a function. (Try, for example, (!PrimeQ)[3] )

You need to use

  !PrimeQ[#]& (* or Not[PrimeQ[#]]& as suggested by @b.gatessucks *)

or

  Composition[Not,PrimeQ]

Then

 NestWhileList[((#1 - 1)*FactorInteger[#1][[1, 1]] + 1) &, 6, 
 Composition[Not, PrimeQ]]

gives

{6, 11}

as expected.

To take another example:

 Select[Range[5], !EvenQ]
 (* {} *)

while

 Select[Range[5], Not[EvenQ[#]]&]
 (* { 1, 3,5 }*)