Billboard Challenge, Part 2
June 26, 2012
In the previous exercise, we looked at a programming challenge that involved the digits of e. Solving that exercise and clicking on the indicated web site took the solver to this page:
Congratulations. You've made it to level 2. Go to www.Linux.org and enter Bobsyouruncle as the login and the answer to this equation as the password.
f(1)= 7182818284
f(2)= 8182845904
f(3)= 8747135266
f(4)= 7427466391
f(5)= __________
Don’t try to login; the account no longer exists.
Your task is to write a program to find the next number in the sequence. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
[…] today’s Programming Praxis challenge, our goal is to solve the second part of the billboard test, which is […]
My Haskell solution (see http://bonsaicode.wordpress.com/2012/06/26/programming-praxis-billboard-challenge-part-2/ for a version with comments):
The difficulty with these kinds of problems is that the given terms often do not identify a unique sequence.
For example, I determined that the values for f(1), f(2), f(3), and f(4) start at position 2, 6, 24, and 100, respectively, in the digits of e. After a few minutes at OEIS.org, I discovered that the differences between successive indices–2, 4, 18, 76–correspond to the first few even Lucas numbers. So I whipped up the following Python code to calculate f(5):
Which results in the following output:
f(1) = 7182818284
f(2) = 8182845904
f(3) = 8747135266
f(4) = 7427466391
f(5) = 4637721112
If you’ve looked at the Praxis solution, this is not the answer they were looking for.
Mike: Yes, that’s a problem.
My solution also differs from the suggested solution at A095926, because I require all numbers to be ten digits long, as in the first challenge problem, but the OEIS solution permits leading zero.