One less than twice its reverse

Sheldon had a monologue with his friends once during a meal, about why 73 is the best number. I dived into this number in a separate post. He was attempting to have a pleasant conversation, but they were not as thrilled as him about recreational mathematics. Too bad, it really is exciting. Anyway, a fact about the number 73 he didn’t mention increased my interest for the number.

It was during a conversation with my mom, who happens to be exactly 73 years old at the time of writing this. I asked her if she wanted to hear a fun fact about that number, and to be honest, I might have felt a little like Sheldon did at that moment. I told her “73 is one less than twice its reverse.” She laughed and said “you must be the only person who thinks about these things”.

The reverse of 73 is 37. Twice of 37 is 74, one more than 73. To repeat, 73 is one less than twice its reverse. Now, this is a fun and exciting discovery I think. Even more so because 73 is the lowest such case, besides 1, which also is one less than twice its reverse. So my mom’s age really is special. And yes, it is indeed a prime number like Sheldon pointed out.

73 is perhaps the lowest such number, but are there other ones below 10.000 or one million?

A little python script can help exploring the depth of this ocean, and yes, there are more. Curiously, they seem to follow a pattern:

73, 793, 7993, 79993, 799993, 7999993, …

" Curiouser and curiouser", said Alice.

I turned to OEIS, The On-Line Encyclopedia of Integer Sequences, which has a record of this sequence, just formulated a little different: numbers k such that 2*reverse(k) - k = 1, but is is the same.

I prefer the wording: One less than twice its reverse, as it has a more riddle-like quality to it, a touch of mystery.