Today, Oct. 31, 2018, is Halloween, and I constructed the following numerical curiosities to celebrate it:
1. Halloween coincides with the 304th day of each non-leap year (e.g., 2018), and I refer to 304 as a spooky number. The reason is because 304 equals the product of numbers 16 and 19. It also equals to twice the sum of the reverses of numbers 16 and 19, namely 61 and 91.
2. Halloween, Oct. 31, expressed as 10/31 or simply 1031, can be written in terms of the first six prime numbers using basic arithmetic as 1031 = 2 x 3 x 5 + 7 x 11 x 13. Furthermore, one of my students, Hailey Diment, pointed out to my attention in class that the sum of 2, 3 and 5 gives 10 and the sum of 7, 11 and 13 yields 31. Great job in making this observation, Hailey!
3. Halloween this year occurs on 10/31/2018 and if this date is split as 10, 31 and 2018. 2018 is twice 1009, 1009 is the 169th prime number, the square-root of 169 is 13, the 13th prime number is 41 and interestingly, 41 equals 10 plus 31. Wow!
4. Halloween in 2021, expressed as 10/31/2021, will be special since the rightmost two digits of 2021, namely 21, equals the difference of 10 and 31, and 20 plus 21 equals 10 plus 31.
5. Halloween in 2028, expressed as 10/31/2028, will also be special because if 10312028 is split as 10, 31, 2028, the 10th and 31st prime numbers are 29 and 127 and their sum equals 156. Again, the sum of 10 and 31 equals 41 and 41 is the 13th prime number. Interestingly, the product of 156 and 13 equals 2028.
6. Additionally, 13 times its reverse, namely 31, equals 403 and the reverse of 403 is 304 (see item # 1).
7. Halloween in 2041, written as 10/31/41, will be special too since 10 plus 31 equals 41. Moreover, if 2041 is split as 20 and 41, 20 plus 41 equals 61 and 61 equals the number of days left in each year after Halloween.
8. Halloween coincides with the 305th day of each leap year (e.g., 2020) and interestingly, 305 equals 61 times the difference of the digits of 61, namely 5.
9. Halloween in 2058, expressed as 10/31/2058, will be special too since the difference of the squares of 10 and 31 equals 861, and twice the sum of 861 and its reverse, namely 168, yields 2058.
10. Lastly, Halloween in 2062, expressed as 10/31/2062, will be very special indeed since 2062 is twice 1031.
Happy Halloween!
Aziz Inan is a professor and chair of electrical engineering program at University of Portland and he can be reached at ainan@up.edu.
