Reversed Multiples

Computer Science Level 5

Let the reverse of a positive integer \(n\), denoted \(R(n),\) be the result when the digits of the number are written backwards; for example, \(R(190) = 091,\) or just \(91.\)

Call a positive integer \(n\) brilliant if \[n + R(n)\]

is a multiple of 13. Let \(B\) be the \(10000\)th brilliant number. Compute the last three digits of \(B.\)

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