Get a list of function results until result > x - fibonacci

Question

I basically want the same thing as this OP:
Is there a J idiom for adding to a list until a certain condition is met?
But I cant get the answers to work with OP's function or my own.
I will rephrase the question and write about the answers at the bottom.
I am trying to create a function that will return a list of fibonacci numbers less than 2.000.000. (without writing "while" inside the function).
Here is what i have tried:
First, i picked a way to culculate fibonacci numbers from this site:
https://code.jsoftware.com/wiki/Essays/Fibonacci_Sequence
fib =: (i. +/ .! i.#-)"0
echo fib i.10
0 1 1 2 3 5 8 13 21 34
Then I made an arbitrary list I knew was larger than what I needed. :
fiblist =: (fib i.40) NB. THIS IS A BAD SOLUTION!
Finally, I removed the numbers that were greater than what I needed:
result =: (fiblist < 2e6) # fiblist
echo result
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040 1.34627e6
This gets the right result, but is there a way to avoid using some arbitrary number like
40 in "fib i.40" ?
I would like to write a function, such that "func 2e6" returns the list of fibonacci numbers below 2.000.000. (without writing "while" inside the function).
echo func 2e6
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040 1.34627e6
here are the answers from the other question:
first answer:
2 *^:(100&>#:])^:_"0 (1 3 5 7 9 11)
128 192 160 112 144 176
second answer:
+:^:(100&>)^:(<_) ] 3
3 6 12 24 48 96 192
As I understand it, I just need to replace the functions used in the answers, but i dont see how
that can work. For example, if I try:
echo (, [: +/ _2&{.)^:(100&>#:])^:_ i.2
I get an error.

Answer 1

I approached it this way. First I want to have a way of generating the nth Fibonacci number, and I used f0b from your link to the Jsoftware Essays.
f0b=: (-&2 +&$: -&1) ^: (1&<) M.
Once I had that I just want to put it into a verb that will check to see if the result of f0b is less than a certain amount (I used 1000) and if it was then I incremented the input and went through the process again. This is the ($:#:>:) part. $: is Self-Reference. The right 0 argument is the starting point for generating the sequence.
($:#:>: ^: (1000 > f0b)) 0
17
This tells me that the 17th Fibonacci number is the largest one less than my limit. I use that information to generate the Fibonacci numbers by applying f0b to each item in i. ($:#:>: ^: (1000 > f0b)) 0 by using rank 0 (fob"0)
f0b"0 i. ($:#:>: ^: (1000 > f0b)) 0
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987
In your case you wanted the ones under 2000000
f0b"0 i. ($:#:>: ^: (2000000 > f0b)) 0
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040 1346269
... and then I realized that you wanted a verb to be able to answer your original question. I went with dyadic where the left argument is the limit and the right argument generates the sequence. Same idea but I was able to make use of some hooks when I went to the tacit form. (> f0b) checks if the result of f0b is under the limit and ($: >:) increments the right argument while allowing the left argument to remain for $:
2000000 (($: >:) ^: (> f0b)) 0
32
fnum=: (($: >:) ^: (> f0b))
2000000 fnum 0
32
f0b"0 i. 2000000 fnum 0
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040 1346269
I have little doubt that others will come up with better solutions, but this is what I cobbled together tonight.