OK, @TfL requires faking UK phone number for Oyster card registration. This error doesn't explain rejecting 16505552368 or 0016505552368.
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Replying to @davidbaron @TfL
For the record, the phone number comes from en.wikipedia.org/wiki/Fictit… . And they also require a UK postcode.

Jul 31, 2017 · 1:04 PM UTC

1
Replying to @davidbaron @TfL
Turns out that having a UK number (from 3) seems a bit handy, I found out after buying one that it allows local cost roaming in Europe.