Oppenheimer Numbers
Abstract
The Oppenheimer numbers problem came from the Math Horizons journal by the MAA. Oppenheimer numbers are a unique class of 2n-digit numbers meeting specific greatest common divisor and divisibility criteria. To solve this problem, we started by making 4-digit Oppenheimer numbers by hand, using the rules provided to us. We quickly realized that this was not the most efficient way to find Oppenheimer numbers. So, one of our group members made a Python program that found all 4-digit Oppenheimer numbers. We then extended our search to 6-digit and 8-digit Oppenheimer numbers, confirming the existence of many such numbers. With all the 4-digit, 6-digit, and 8-digit Oppenheimer numbers before us we looked for patterns in our dataset. We were able to identify patterns such as every Oppenheimer number started with either a 3, 7, or 9. We further proved that for every n ≥ 2, there is at least one 2n-digit Oppenheimer number.
Oppenheimer Numbers
PENNY 203
The Oppenheimer numbers problem came from the Math Horizons journal by the MAA. Oppenheimer numbers are a unique class of 2n-digit numbers meeting specific greatest common divisor and divisibility criteria. To solve this problem, we started by making 4-digit Oppenheimer numbers by hand, using the rules provided to us. We quickly realized that this was not the most efficient way to find Oppenheimer numbers. So, one of our group members made a Python program that found all 4-digit Oppenheimer numbers. We then extended our search to 6-digit and 8-digit Oppenheimer numbers, confirming the existence of many such numbers. With all the 4-digit, 6-digit, and 8-digit Oppenheimer numbers before us we looked for patterns in our dataset. We were able to identify patterns such as every Oppenheimer number started with either a 3, 7, or 9. We further proved that for every n ≥ 2, there is at least one 2n-digit Oppenheimer number.
