# 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? – Hugh Jan 8 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 :) – zennehoy Jan 8 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. – Excited Raichu Jan 8 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? – Hugh Jan 8 at 15:46
• @Hugh see my edit – rhsquared Jan 8 at 15:53
• Don't overthink it :) – zennehoy Jan 8 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. – snetch Jan 8 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. – Michael Seifert Jan 8 at 19:43