with "Using Exact Arithmetic" --by CliffReiter Department ofMathematics Lafayette College,Easton, Pennsylvania that I ever explored on my own using a computer was the question of whether the integer 196, under addition to digit reversals, ever led to a palindrome. This is a recreational math problem that has been around for awhile [2]. A palindrome is a number which is the same upon reversal of its digits. Thus 17471 is a palindrome while 17414 is not. Under the process of adding numbers to their reversals, most numbers quickly seem to yield a palindrome; for example, when beginning with 37, we add 37 to 73 to get the second number 110. Then 110 plus 011 gives 121, which is a palindrome. The beginning of the sequence that starts with 196 is "196 887 1675 7436 2^lOOrl 1267650600228229401496703205376 2 ^ x: i00 1267650600228229401496703205376 2%3 0.666667 2r3 2r3 i+2r3 5r3 x: 2 % 3 2r3 x: 0 . 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 2r3 x: 0 . 6 6 6 6 7 66667ri00000 T HE FIRST MATHEMATICAL QUESTION The last example illustrates that we still need to be careful to think
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With J: using exact arithmetic
Reiter, Cliff
Follow ACM SIGAPL APL Quote Quad
, Volume 28 (3)
Association for Computing Machinery – Mar 1, 1998
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