This is the sequence of numbers n such that 3 times the reversal of n plus 1 is the number itself. In other words, n = 3*reversal(n)+1. For example, 742 = 3*247+1. In fact, 742 is the smallest number with this property. How does this sequence continue, and why?

I figured out that 783742162 is another number in the sequence. So is 783783742162162. In fact, you can keep tacking 783’s at the start and 162’s at the end, and thus get infinitely many such numbers.

Are those (with 742) all the numbers in the sequence? I don’t know, but I’m guessing yes, since otherwise you probably wouldn’t have asked this question. ðŸ™‚

## Joseph:

I figured out that 783742162 is another number in the sequence. So is 783783742162162. In fact, you can keep tacking 783’s at the start and 162’s at the end, and thus get infinitely many such numbers.

Are those (with 742) all the numbers in the sequence? I don’t know, but I’m guessing yes, since otherwise you probably wouldn’t have asked this question. ðŸ™‚

19 July 2021, 10:12 pm## Piotr:

It seems that the answer is all numbers A that can be generated (recursively) by the following productions:

A -> 742 | 742B742 | 783A162

B -> 5 | 162B783 | 5A5

So the first few are:

742

22 July 2021, 7:56 pm7425742

783742162

74257425742

7421625783742

7837425742162

742574257425742

783783742162162

74216257425783742

74257837421625742

78374257425742162