numbers 1 4 6 8 9 10 12 14 15 16 27 34 49 56 57 58 70 all have or lack a certain property. any ideas i'm lost???

To find the property that these numbers either have or lack, let's examine the sequence more closely.

1 4 6 8 9 10 12 14 15 16 27 34 49 56 57 58 70

First, let's identify any patterns or relationships within the sequence. One way to start is by looking at the differences between consecutive terms:

3 2 2 1 1 2 2 1 1 11 7 15 7 1 1 12

Observing the differences, we can notice a few things:

1. There are repeating patterns within the differences, such as 2-1-2-1.
2. There are larger jumps, like 11-7-15, that are not part of the repeating pattern.

Now, let's pay attention to the repeating pattern "2-1-2-1". Notice that this pattern starts after the first two terms, 3 and 2, which suggests that the property may involve skipping the first two numbers.

If we skip the first two numbers and apply the repeating pattern, we get:

6 8 9 10 12 14 15 16 27 34 49 56 57 58 70

Indeed, the sequence continues just as expected. Therefore, the property appears to be that the numbers either have or lack the feature of skipping the first two terms (1 and 4), and then incrementing and decrementing alternately with a difference of 1.

In summary, the property of the given sequence is that the numbers either have or lack the feature of skipping the first two terms and then incrementing and decrementing alternately with a difference of 1.