number pattern?

Question

1, 2, 5, 10, 21

do you guys see a pattern here? if so, what is it?

Answer 1

42
85
170
341
682
1365
2730
5461

alternate terms are double the previous term and then double the previous term plus add one.

Answer 2

I do not see a simple pattern. Perhaps the pattern is alternately double, or double and add one?

1
1*2 = 2
2*2 + 1 = 5
5*2 = 10
10*2 + 1 = 21

The next numbers in the pattern would be 42, 85, 170, 341.

Answer 3

In the series 1,2,5,10,21, alternate steps are doubling
versus doubling and adding one.

Thus 1 -> 2 by doubling, 2 -> 5 by doubling and adding one,
5 -> 10 by doubling, and 10 -> 21 by doubling and adding one.

So the next numbers will be 42, 85, 170, etc.

Answer 4

If the number is odd, double it. if it is even, double and add one?

1 is odd, double it to get 2
2 is even, double and add 2 to get 5.
etc.
the next number will be 42

Answer 5

k, Nk
-------------
1, 1 or 1
2, 2, k
3, 2^2+1,
4, 2^3+2
5, 2^4+5, 2^(k-1)+k


It looks like Nk = 2^(k-1)+k , almost!