1,1

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.

Tanya Khovanova, Non Recursions

A safety or 2 points is the minimum possible sum of scores at the end of a

game. So if a team shuts out the other with a safety, the sum of their scores

is 2.

Sequence in context: A008684 A138202 A056064 this_sequence A024000 A097141 A038608

Adjacent sequences: A114139 A114140 A114141 this_sequence A114143 A114144 A114145

easy,nonn

Cino Hilliard (hillcino368(AT)gmail.com), Feb 03 2006