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In 2000, Florian Luca proved that F10 = 55 and L5 = 11 are the largest numbers with only one distinct digit in the Fibonacci and Lucas sequence, respectively. In this paper, we find terms of a linear recurrence sequence with only one block of digits in its expansion in base g ≥ 2. As an application, we generalize Luca’s result by finding the Fibonacci and Lucas numbers with only one distinct block of digits of length up to 10 in its decimal expansion.

On terms of linear recurrence sequences with only one distinct block of digits