Write a continuous quine (quine-variant)

Question

Let's define a 2-quine as a program that prints its source code two times. For example, if the program ABC printed ABCABC, it would be a 2-quine.

Let's define a 3-quine as a program that prints its source code three times. For example, if the program ABC printed ABCABCABC, it would be a 3-quine.

Let's define a n-quine as a program that prints its source code n times.

Your task is to write a 2-quine, that prints a 3-quine, that prints a 4-quine, that prints a 5-quine, etc...

For example, here is an example of a valid submission (which is fictional of course):

AB

which prints

ABAB

which prints

ABABABABABAB

which prints

ABABABABABABABABABABABABABABABABABABABABABABABAB

etc.

Remember, this is code-golf, so the program with the fewest bytes wins.

Answer 1

QBasic (224 bytes incl. trailing CR+LF)

(Tested with QBasic/MS-DOS on a virtual machine as well as with FreeBASIC with "-lang qb" setting)

a$="a$=:l=l+1:if l>y then f=f+1:y=y*f+y+f:while x<=y:x=x+1:print mid$(a$,1,3)+chr$(34)+a$+chr$(34)+mid$(a$,4):wend":l=l+1:if l>y then f=f+1:y=y*f+y+f:while x<=y:x=x+1:print mid$(a$,1,3)+chr$(34)+a$+chr$(34)+mid$(a$,4):wend

Answer 2

Javascript ES6 (REPL), 52 bytes

var a=a||'';$=_=>a+=`$=${$};$();`.repeat(a?1:2);$();

Initial working implementation, may be golfable.

y.onclick=_=>z.innerText=eval("var a=a||'';$=_=>a+=`$=${$};$();`.repeat(a?1:2);$();".repeat(x.value))

<input id=x><button id=y>Submit!</button><pre id=z></pre>

Explanation

Based on my usual quine implementation ($=_=>`$=${$};$()`;$()).

var a||'' coerces a to an empty string if it isn't defined; otherwise, a is left as is. a will store our final result.

Each function call, a will be checked to see if it is empty/falsy. The first function call will append 2 copies of the quine because a is empty; subsequent calls will only append 1 copy because a is no longer empty.

The last function call will output the final value of a after finishing.

Answer 3

Ruby, 154 bytes

s=DATA.read.lines;s+=s[0,2];n=s.size/4;k=1;n/=k+=1while n>0;puts s*k
__END__
s=DATA.read.lines;s+=s[0,2];n=s.size/4;k=1;n/=k+=1while n>0;puts s*k
__END__

The trailing newline matters.

This program first duplicates itself; the output triplicates itself; that output quadruplicates itself, etc.

Thus the n-th program is a repetition of these 4 lines, n! times.

s=DATA.read.lines;s+=s[0,2]; gets us the current source code as an array of lines. We take its length, divide it by 4, compute the inverse factorial, add one, then print s that many times.