Chapter 11
Link: Online Encyclopaedia of Integer Sequences
The OEIS is an invaluable reference for anyone wanting to find out about sequences of integers. Type in the first few terms to see which sequences start with them or type in the name of a sequence to find it in the database. Look up your birthday! Or, you know, use it for serious mathematical research.
Online Encyclopaedia of Integer Sequences (website)
Toy: Combination Calculator
Are you faced with a pile of M things from which you need to choose N? We’ve all been there. And this handy calculator will tell you exactly how many options you have. (Full version)
Chapter 12
Link: Domino computer worksheets
Put your spare dominoes to good use doing some incredibly slow calculations. Over at Think Maths (my education site) I have a great selection of worksheets outlining how to build different domino logic gates, so you can give it a try!
Think Maths Domino Computer Worksheets (website)
Chapter 13
Matt’s Python code
It’s not pretty and it’s not efficient, but here is my python code for finding grafting numbers is below. I wrote it when I was learning Python as a hobby. If you know how to run Python code, you can use it to find grafting numbers for yourself!
Click to show/hide Matt’s code
# Just trying to find the 764 chain
r = 2
n = 760
find = 9
interest = 0
found = 0
run1 = 1
list764 = []
while run1 == 1:
run2 = 1
n = n+1
root = n ** (1./r) #the r'th root
if n == (int(root)) ** r: #this bit moves it along if n is a perfect square, cube etc
n = n + 1
root = n ** (1./r)
length = len(str(n)) #length of number being tested
lead = len(str(int(root))) #number of leading digits
test = root * (10 ** (length -lead))
pos = -lead #77 should have a pos of 0
while run2 == 1:
t = int(test)
if n == t:
print 'Found {0} at position {1}'.format(n, pos)
list764.append(n)
found = found + 1
n = 100*(n-100)
run2 = 0
test = 10*test-(10 ** length)*int(test*(1./(10 ** (length-1))))
pos = pos+1
if pos > interest:
run2 = 0
if found == find:
print "finished"
print list764
run1 = 0