Question

What comes next in the sequence: 1, 3, 11, 43, ____?
161
171
181
191

Answer 1

any specific formula to find out sequence?

Answer 2

\[1\color{red}{+2},3\color{red}{+8},11\color{red}{+32},43\]see a pattern?

Answer 3

Hint: \[2^1 = 2, 2^3 = 8, 2^5 = 32, 2^7 = 128\]

Answer 4

hmm

Answer 5

but correct ans is 171

Answer 6

The powers of 2 in my list correspond to the red numbers in @doc.brown 's list

Answer 7

That's right, the correct answer is 171. Follow the pattern in both of our lists to get 171.

Answer 8

ok ok

Answer 9

You know you are increasing the powers of 2 by odds because of the established pattern from 1-> 3 -> 5

Answer 10

OP left

Answer 11

I always try increasing the numbers in an addy kind of way, if that doesn't work, try increasing the numbers in a timesy kind of way.\[1\color{blue}{\times3},3\color{blue}{\times3\frac{2}{3}},11\color{blue}{\times3\frac{909}{1000}},43\]Which is even less helpful in this case, but I wanted to show you.

Answer 12

\[\text{Table}\left[\frac{1}{6} \left(2^{2 n}+2\right),\{n,8\}\right]=\{1,3,11,43,171,683,2731,10923\} \]