1, 4, 9, 61, 52, 63, 94, what next?

Question

Find the rule and the next term of 1, 4, 9, 61, 52, 63, 94, ? The sequence begins like something very familiar and then seems to go wrong at the fourth term. Explain what is really happening, and give the two terms after the missing one as well.

Accepted Answer

The next term is 46. Each term is a square number with its digits reversed. Check. The squares are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Reversing the digits gives 1, 4, 9, 61, 52, 63, 94, 46, 18, 001. So the next term is 46, then 18, then 1 (from 100 reversed, dropping the leading zeros). How to spot it. The start 1, 4, 9 screams "squares", and the failure at 61 instead of 16 is the tell: 61 is 16 backwards. Whenever a familiar sequence goes wrong at exactly the point where its terms acquire a second digit, suspect a digit manipulation: reversal, digit sum, digits sorted, or digits in anothe…

1, 4, 9, 61, 52, 63, 94, what next?

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