%I A114142
%S A114142 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,
%T A114142 28,29,30,31,32,33,34,35,36,37,38,39,40
%N A114142 Possible sums of the final scores of completed Chicago Bears football 
               games.
%C A114142 1 point only is an impossible score in American football. But with the 
               safety 2 and the field goal 3, we can construct the set of integers 
               greater than 1. We can prove this by noting that if a score is even, 
               we can build it with a series of safeties. Of course the other scorings 
               allowed of 3,6 and 1 after a touchdown, could also be used. Now if 
               a score is odd it is of the form 2k+3. So for any odd number 2m+1, 
               we subtract 3 or 1 field goal from it to make it even and divide 
               by 2 to get the number of safeties we need to add back to the field 
               goal. Symbolically, let the odd number be 2m+1. then (2m+1 - 3)/2 
               = m-1 safeties needed. Add this to 3 and you will have the number. 
               For example, say we want a score of 99. 99 = 2m+1 and m = 49. So 
               m-1 = 48 safeties + 1 field goal = 99 points.
%H A114142 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               NonRecursions.html">Non Recursions</a>
%e A114142 A safety or 2 points is the minimum possible sum of scores at the end 
               of a
%e A114142 game. So if a team shuts out the other with a safety, the sum of their 
               scores
%e A114142 is 2.
%Y A114142 Sequence in context: A008684 A138202 A056064 this_sequence A024000 A097141 
               A160356
%Y A114142 Adjacent sequences: A114139 A114140 A114141 this_sequence A114143 A114144 
               A114145
%K A114142 easy,nonn
%O A114142 1,1
%A A114142 Cino Hilliard (hillcino368(AT)gmail.com), Feb 03 2006