Continue the Sequence: 742, …

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?

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2 Comments

  1. 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. 🙂

  2. 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
    7425742
    783742162
    74257425742
    7421625783742
    7837425742162
    742574257425742
    783783742162162
    74216257425783742
    74257837421625742
    78374257425742162

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