Using the "graph" function to debug sequences

[Brendan McKay]

Hugo Pfoertner noticed that the log scatterplot of A007022 shows an
odd little kink at n=31.  Not all sequences necessarily give a smooth
curve, of course, but a great many do.  A kink like this is a possible
indication that something is amiss, and in this case it is indeed
an error.  The original document this sequence came from has two
numbers interchanged.

The wrong value is in fact high by close to a factor of 2. This can
be seen even more obviously by plotting A007022(n+1)/A007022(n) on
the plot2 page. This would be able to detect even a much smaller error.

So, the moral of the story is that these plots are not just pretty
faces but can actually help to get sequences correct.  Thanks to Hugo
for finding this example.

http://www.research.att.com/~njas/sequences/A007022
http://www.research.att.com/~njas/sequences/plot2.html

Cheers, Brendan.