you can start with one numbersay and keep applying the jump function to the last number givenand see how the numbers jump aroundjump( * + jump( // jump( * + jump( // jump( // jump( // jump( // this process of repeatedly applying the same function to the most recent result is called function iteration in this case you see that iterating the jump functionstarting from = eventually reaches the value it is an open research question whether iterating the jump function from an integer will eventually reach for every starting integer greater than researchers have only found examples of where it is true stillno general argument has been made to apply to the infinite number of possible starting integers in this exercise you iterate the jump function for specific starting values nuntil the result is save example jumpseqstub py as jumpseq py and complete the missing function bodies if you coded the function jump before in jumpfunc pyyou can copy it you can complete either printjumps or listjumps firstand test before completing the other hint after you have finished and saved jumpseq py copy it and save the file as jumpseqlengths py first modify the main method so it prompts the user for value of nand then prints just the length of the iterative sequence from listjumps(nhint then elaborate the program so it prompts the user for two integersa lowest starting value of and highest starting value of for all integers in the range from the lowest start through the highest startincluding the highestprint sentence giving the starting value of and the length of the list from listjumps(nan example runenter lowest start enter highest start starting from jump sequence length starting from jump sequence length starting from jump sequence length starting from jump sequence length graphical applications another place where while loop could be useful is in interactive graphics suppose you want the user to be able to create polygon by clicking on vertices they choose interactivelybut you do not want them to have to count the number of vertices ahead of time while loop is suggested for such repetitive process as with entering lines of text interactivelythere is the question of how to indicate that you are done (or how to indicate to continueif you make only certain region be allowed for the polygonthen the sentinel can be mouse click outside the region the earlier interactive color choice example already has method to check if mouse click is inside rectangleso that method can be copied and reused creating polygon is unified activity with clear resultso let' define function it involves boundary rectangle and mouse clicks in graphwinand may as well return the polygon constructed read the following startdef polyhere(rectwin)''draw polygon interactively in rectangle rectin graphwin win collect mouse clicks inside rect into the vertices of polygon you will need loop you can print/append almost all the numbers in the loop you are likely to omit one number with just this codebut after looking at what you produceit is easy to separately include the remaining number there are several ways to do this recall the built-in len functionit applies to lists while statements