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$\begingroup$

... 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?

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  • $\begingroup$ Is this a puzzle of your own creation? $\endgroup$
    – user46002
    Jan 8, 2019 at 15:11
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    $\begingroup$ @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 :) $\endgroup$
    – zennehoy
    Jan 8, 2019 at 15:20
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    $\begingroup$ 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. $\endgroup$ Jan 8, 2019 at 15:39

1 Answer 1

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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.

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  • 2
    $\begingroup$ So, the sequence is: "numbers in base-10 that equal themselves backwards in base-8"? What could cause this gap? $\endgroup$
    – user46002
    Jan 8, 2019 at 15:46
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    $\begingroup$ @Hugh see my edit $\endgroup$
    – rhsquared
    Jan 8, 2019 at 15:53
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    $\begingroup$ Don't overthink it :) $\endgroup$
    – zennehoy
    Jan 8, 2019 at 15:56
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    $\begingroup$ @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. $\endgroup$
    – snetch
    Jan 8, 2019 at 18:34
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    $\begingroup$ @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. $\endgroup$ Jan 8, 2019 at 19:43

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