N terms of Van Eck sequence with custom 1st term

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#1

I want to generate iterations terms of a Van Eck sequence with a custom starting term.

The result of the function is an incorrect sequence and I have no clue why.
I’ve tried looking at the Rosetta Code example’s, but the code for the solutions don’t make sense to me.

I understand how to do the sequence on paper, but I’m really struggling to implement it into code for some reason.

Here is my current code:

local function van(number, iterations)
    local sequence = {}
    local positions = {}

    for i = 1, iterations do
        local last = positions[number]

        if (last) then
            number = i - last
        else
            number = 0
        end

        sequence[i] = number
        positions[number] = i
    end

    return sequence
end

local sequence = van(0, 9)

print(table.concat(sequence, ", "))

And the outputted sequence: 0, 1, 1, 1, 1, 1, 1, 1, 1
And here is what it should output: 0, 0, 1, 0, 2, 0, 2, 2, 1, 6

#2

I’ve remade your code with a bunch of debug prints so you can easily figure out what is happening :slight_smile:
Not exactly sure what makes your code break but I believe it’s positions[number] = i giving the wrong position of the last position.

local function van(number, iterations)
	local sequence = {}
	local prevPos = {}
	local lastPos = {}
	
	local wasFirstOne = false
	
	for i = 1, iterations do
		print("checking number ", number)
		
		if wasFirstOne then
			print("before it was the first one")
			number = 0
			wasFirstOne = false
		else
			if lastPos[number] then
				print("found it before at pos ", prevPos[number])
				number = i - prevPos[number] - 1
				
				if not lastPos[number] then
					print("but hey,", number, "wasn't found before")
					wasFirstOne = true
				end
			else
				print("wow it was the first one")
				wasFirstOne = true
			end
		end
		
		sequence[i] = number
		prevPos[number] = lastPos[number]
		lastPos[number] = i
		
		print(table.concat(sequence, ", "))
		
		print("--------")
	end
	
    return sequence
end

local sequence = van(0, 10)

print(table.concat(sequence, ", "))

I used this video to figure out what is happening with the algorithm, perhaps it may also help you.

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