Palindrome and Prime
93639 (a palindromic number) plus the sum of its prime factors is equal to 93683, which is a prime number:
93683 = 93639 + 3 + 7 + 7 + 7 + 7 + 13
Interestingly, there is no prime number between 93639 and 93683.
And it Continues…
(15 + 25) + (17 + 27) = 2 (1 + 2)4
(15 + 25 + 35) + (17 + 27 + 37) = 2 (1 + 2 + 3)4
(15 + 25 + 35 + 45) + (17 + 27 + 37 + 47) = 2 (1 + 2 + 3 + 4)4
(15 + 25 + 35 + 45 + 55) + (17 + 27 + 37 + 47 + 57) = 2 (1 + 2 + 3 + 4 + 5)4
etc.
Power Relationships
6205 = 38² + 69² and 3869 = 62² + 05²
5965 = 77² + 06² and 7706 = 59² + 65²
The following is less obvious and it involves cubes instead of squares:
244 = 1³ + 3³ + 6³ and 136 = 2³ + 4³ + 4³
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Nice!! I love math!!
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:)
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Nice. I don’t know if you’ve done a post on amicable numbers yet:
https://en.wikipedia.org/wiki/Amicable_numbers
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I’ll do a post about it in the future.
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