### Brain Teasers

# 1, 3, 7, 11, 17, 23, 31, 50, 60, 71, ...

What are the next five terms in this sequence?

1, 3, 7, 11, 17, 23, 31, 50, 60, 71, 83, 97, 111, 127, 153, 171, 190, 210, 231, 263, 287, 311, 337, 373, ___, ___, ___, ___, ___, ...

1, 3, 7, 11, 17, 23, 31, 50, 60, 71, 83, 97, 111, 127, 153, 171, 190, 210, 231, 263, 287, 311, 337, 373, ___, ___, ___, ___, ___, ...

### Hint

1111, 11111, 111111, ... will also appear in this sequence.### Answer

501, 530, 570, 601, 633.In all the natural numbers that don't contain the "unlucky" digit 4, the first one is 1, skip one and get 3, skip two and get 7, skip three and get 11, and so on.

It can also be said that these are the triangular numbers in the nonary system, except that the digits 0, 1, 2, 3, 5, 6, 7, 8, 9 are being used to represent 0, 1, 2, 3, 4, 5, 6, 7, 8.

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