# That gap is a bit jarring

... but there doesn't seem to be anything missing.

$$0,1,2,3,4,5,6,7,1527465$$

What then could cause that rather large gap?

• Is this a puzzle of your own creation? Jan 8, 2019 at 15:11
• @Hugh I came across the sequence more or less by accident, and was surprised that it wasn't on OEIS yet. I figured I'd post it here before adding it there :) Jan 8, 2019 at 15:20
• They're the solutions to the polynomial x^9 - 1527493x^8 + 42769342x^7 - 49185690x^6 + 2993838169x^5 - 10339423717x^4 + 20058670380x^3 - 5040x^2 + 7698423600x = 0, but for some reason I doubt that's the cause. Jan 8, 2019 at 15:39

## 1 Answer

The sequence 0,1,2,3,4,5,6,7 pointed towards octal numbers.
If we take the number 1527465 (base 10) and convert it to base 8 we get the same digits in reverse order 5647251
The gap is because no other number between 7 and 1527465 shares that property.

• So, the sequence is: "numbers in base-10 that equal themselves backwards in base-8"? What could cause this gap? Jan 8, 2019 at 15:46
• @Hugh see my edit Jan 8, 2019 at 15:53
• Don't overthink it :) Jan 8, 2019 at 15:56
• @Hugh just brute forced it all the way through 10,000,000 and you're right, these eight numbers are the only ones that reverse into their octal counterparts. Jan 8, 2019 at 18:34
• @snetch: Note that any such numbers must be less than 10^10, since any 10-digit number in base 10 will have at least 11 digits in base 8. Jan 8, 2019 at 19:43