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Background
A167519: Lexicographically earliest increasing sequence which lists the positions of the zero digits in the sequence.
3, 10, 11, 12, 11000, 11111, 11112, 11113, 11114, 11115, 11116, 11117, 11118, 11119,
11121, 11122, 11123, 11124, 11125, 11126, 11127, 11128, 11129, 11131, 11132, 1113...