How can I print only the lines for a file that contain consecutive digits?

Question

I have a text file containing a list of numbers. I want to print only the lines that contain a number, the digits of which are consecutive digits.

The input list:

123
321
567
765
124
568

The output should be:

123
321
567
765

Answer 1

consecutive = Total[Abs[Differences[IntegerDigits@FromDigits@#]] - 1] &;
string = "123 321 567 765 124 568";
Pick[#,  consecutive /@ #, 0]& @ StringSplit[string]

{"123", "321", "567", "765"}