# Takes a tape representing a natural number k (see Boolos, Burgess
# and Jeffrey for definition) and returns a tape representing a pair
# <k,k>.

(0,1, ,1,r) 
(0, , ,2,r) 
(1, , ,3,r)  # Look for blank
(1,1,1,1,r) 
(3, ,1,4,r)  # Wrote my 1.
(3,1,1,3,r) 
(4, , ,5,r) 
(4,1, ,6,r) 
(5, ,1,7,l) 
(6, ,1,8,r) 
(6,1,1,6,4) 
(7, , ,9,l) 
(7,1,1,7,l) 
(8, ,1,7,l) 
(9, , ,10,l) 
(9,1,1,9,l) 
(10, , ,0,r) 
(10,1,1,10,l)