Open "d:/SequentialFile1" for INPUT as #52
Seek #52, Seek(1)

This won't work at all the way you have it, nor for what you're trying to use it for.   Bare with me a bit, as I try and explain these various commands.

SEEK #55, whatever --- this is a SUB which you're calling.  https://wiki.qb64.org/wiki/SEEK_(statement)   It basically is a way to telling the program to move the file pointer to whatever position you want it at.

, Seek(1) ---  this is the FUNCTION which you're calling.  https://wiki.qb64.org/wiki/SEEK  It basically is a way of your programing asking where the file pointer of some file is currently at.

So:  SEEK #52, Seek(1) is basically saying:
Move the file pointer on (filehandle 52) to wherever the file pointer on (filehandle 1) is currently positioned.

Since you don't have an OPEN whateverFile$ FOR INPUT/OUTPUT AS #1, you're going to get an error as there's no open filehandle 1.

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So, that's the FIRST reason why what you're trying isn't going to work.

The second reason is due to you OPENing the file in question FOR INPUT.

SEEK (as the SUB version) will place you directly at whatever byte you want to go to -- it doesn't track record positions at all.   It's only when you OPEN FOR RANDOM, that SEEK will move from one record to the next...

INPUT/OUTPUT/BINARY -- SEEK moves to byte position
RANDOM -- SEEK moves to record position

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So, the only way something like this would be somewhat valid would be if:

OPEN "d:/SequentialFile1" For Random AS #52
Seek #52, Seek(52) + 1   'move to next record

Notice how all my file handles reference the same file, and that it's an Open For Random file?

I'm thinking the above is close to what you're shooting for, but I'm not certain as the original isn't really code which can do anything except error on you.  What exactly are you trying to do with the code here, after all?

OPEN "d:/SequentialFile1" For Random AS #52
Seek #52, 1   'move to first record
Seek #52, 3   'move to third record
Seek #52, Seek(52) + 2   'move two records past the current one

Why use seek with a sequential file, you have to worry about CR and LF chr$(13) chr$(10)... and an EOF marker too I think?

Sequential files best for variable length data.

Running into a bad file name or number error message when using Seek on a sequential file and not sure why.

Open "d:/SequentialFile1" for INPUT as #52
Seek #52, Seek(1)

The above is generating the error message. I have checked the name of the file I'm trying to open, and that the file is indeed on my "d" drive, also that the same opening statement works with Input #52.

I checked the wiki and the example it provides drops the "#" . The wiki has the seek statement as SEEK 1, Seek(1) ( ie there is no "#").

I'm not sure which is the correct statement but no matter, both with or without the "#" I'm getting the error message. I have also tried to be sure the file I'm trying to access is Closed before the Opening statement.

Any idea's on what I could be doing wrong, and which to the two Seek statements is the correct one?

Thanks

Here is my results with qb64 1.5v on win7 32bit

It's fundamentally the wrong idea to rely on _fileexists to say whether or not an IO operation will succeed. The file might exist but you have insufficient permission to open/delete it, another program might remove the file between your program checking and using the file, there may be a network error (if the file is from a network share). A more robust solution is to simply catch the error and respond accordingly:
'At the top of the program
On Error Goto general_error
Dim Shared Error_happened As Long

'Main Program

End
general_error:
Print "Fatal error"; err; "at line"; _errorline
end

io_error:
Error_happened = err
Resume Next

Sub delete_files(names$)
Error_happened = 0
On Error Goto io_error
Kill names$
On Error Goto general_error
If Error_happened then
  'Ignore or inform user, depending on use case
End If
End Sub