Reversed Multiples

Let the reverse of a positive integer nn, denoted R(n),R(n), be the result when the digits of the number are written backwards; for example, R(190)=091,R(190) = 091, or just 91.91.

Call a positive integer nn brilliant if n+R(n)n + R(n)

is a multiple of 13. Let BB be the 1000010000th brilliant number. Compute the last three digits of B.B.

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