On: Infinite Bang Bang

[jamesmaniscalco]

Trying to figure out a mathematical representation of this sequence...

I noticed that different patterns emerge when you subtract 1 from each value in the sequence. From there we get:

0

1

2

4

16

160

15680

159591040

16866847940875520

Each (excluding 0 and 1) is a multiple of the previous term:

1

2 = 1 * 2

4 = 2 * 2

16 = 4 * 4

160 = 16 * 10

15680 = 160 * 98

159591040 = 15680 * 10178

16866847940875520 = 159591040 * 105687938

Anything ring a bell? Notice any other patterns?

[jamesmaniscalco → jamesmaniscalco]

Also, subtracting 2 from each of those numbers produces a similar pattern:

2 - 2 = 0

2 - 2 = 0

4 - 2 = 2

10 - 2 = 8 = 2 * 4

98 - 2 = 96 = 8 * 12

10178 - 2 = 10176 = 96 * 106

105687938 - 2 = 105687936 = 10176 * 10386