- #1

FeDeX_LaTeX

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Can you identify a pattern in this sequence of numbers (a recurrence relation)?

1, 3, 5, 9, 13, 17, 25, 33, 41, 49, 65, 81, 97, 113, 129, 161, 193, 225, 257, 289, 321, 385, 449, 513, 577, 641, 705, 769, 897, 1025, 1153, 1281, 1409, 1537, 1665, 1793, 2049, 2305, 2561, 2817, 3073, 3329, 3585, 3841, 4097, 4609, 5121, 5633...

I can sort of see a pattern but not a recurrence relation... if we look at how we can progressively get from term to term, it looks like this:

2¹ + 2¹ + 2² + 2² + 2² + 2³ + 2³ + 2³ + 2³...

So whenever you end up with a difference of 2

^{n}, you add that difference to any term n+1 times.

But generating a recurrence relation is more difficult...

Can you see a pattern?