A smooth sequence of numbers like 799779977=17*19^6

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I’m told the next term might be 6676767776777676766677777677677 with a highest prime factor of 941.

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Suppose we denote two digits in such numbers simply as 0 and 1 and consider their sequence.
For a number 6676767776777676766677777677677 this is
{0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1}
I wonder what the properties of this sequence are?
Will it be like Thue-Morse, or smth like this…

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