A powerful drink

Question

I'm addicted to this stuff.

I had my first double when I was 16. There were five of us that night on the town. I didn't think much of it then, but two years later I had another double, and then another the following year.

That was when I first realized I might have a problem. I cut it off cold-turkey for the next 3 years, but then it came back with a vengeance. I had a double, then the next year I had a triple. The year after that I had three doubles in a row!

I slowed down a bit after that; only one double a year for the next two years, and then a long dry spell. I only cheated once until I was 38.

Then I fell hard. I had two doubles that year, followed by a double and a triple the next year, then two doubles and a triple. I just had my first quadruple, and I don't know what I'm going to have next year.

Do you?

Answer 1

Next year you're going to have:

a triple.

The references are to:

groups of repeated digits in the number 2^Y, where Y is the year number. Here's a table of results:

16 -> 2^16 = 65536
17 -> 2^17 = 131072
18 -> 2^18 = 262144
19 -> 2^19 = 524288
20 -> 2^20 = 1048576
21 -> 2^21 = 2097152
22 -> 2^22 = 4194304
23 -> 2^23 = 8388608
24 -> 2^24 = 16777216
25 -> 2^25 = 33554432
26 -> 2^26 = 67108864
27 -> 2^27 = 134217728
28 -> 2^28 = 268435456
29 -> 2^29 = 536870912
30 -> 2^30 = 1073741824
31 -> 2^31 = 2147483648
32 -> 2^32 = 4294967296
33 -> 2^33 = 8589934592
34 -> 2^34 = 17179869184
35 -> 2^35 = 34359738368
36 -> 2^36 = 68719476736
37 -> 2^37 = 137438953472
38 -> 2^38 = 274877906944
39 -> 2^39 = 549755813888
40 -> 2^40 = 1099511627776
41 -> 2^41 = 2199023255552
42 -> 2^42 = 4398046511104

Answer 2

Work in progress:

You will have ...

---

Here's a timeline of #s in your habit:

* 16: first double
5 of us that night on town
* 18 double,
* 19 double
first time realized problem
* 20 cut off
* 21 cut off
* 22 cut off
* 23 double
* 24 triple
* 25 three doubles in a row
* 26 one double a yr
* 27 one double a yr
only one cheat until age 38
* 38 two doubles
* 39 double and triple
* 40 had two doubles & a triple
* 41 first quadruple
what will have next year? [42?]

The pattern I notice above is that:

* You can fit 8 in twice once yr=16, when you had your first double
* You can fit in 8 in three times at yr=24, when you had 3 doubles, so maybe double is referring to an operation upon # 4. A 'double' is 4*2=8, 3 doubles is 8*3=24.
Not sure what coherent pattern keeps up throughout this madness yet, however.