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equidigital n.  and  straight-line n.

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(max 15 digits)

First numbers that belong to both sets:

111, 123, 135, 147, 159, 567, 1234, 1357, 2345, 3456, 4567, 11111, 12345, 13579, 23456, 76543, 123456, 1111111, 1234567.