# [Jelly], 16 bytes

    J:g¥’}U×ḷb§¥ƬṪS%

[Try it online!][TIO-lzn1shx9]

[Jelly]: https://github.com/DennisMitchell/jelly
[TIO-lzn1shx9]: https://tio.run/##y0rNyan8/9/LKv3Q0kcNM2tDD09/uGN70qHlh5YeW/Nw56pg1f@Hl@trRv7/Hx0dbaijYKKjYBirY2gUq8MVHW2uY6hjpGOsY6JjqmOmY65joWOpY2igYwlXAORA5eFCyCKGEEUQU4kw2NAAu8mGSCYbw0ViAQ "Jelly – Try It Online"

A less naive computation of the digital roots comes out a bit longer by having to special-case 0. Inverted output: truthy (nonzero) if the checksum fails.

```
J                   1-indices from the start
 :                  divided by
  g¥                their GCDs with
    ’}              B - 1
      U             reversed
       ×ḷ           times each N.
            ƬṪ      Loop while unique:
         b ¥        Convert each to base B
          §         and sum each.
              S     Sum
               %    mod B.
```