# Increasing and Decreasing

1, 0, 3, 11, 15, 13, 17, 24, 23

I believe this is sufficient information to find the 9th through 12th numbers in this sequence

What are the 9th, 10th, 11th, and 12th terms?

• Hope this doesn't turn out to be too broad. Dec 7 '16 at 14:06
• That's my thought Dec 7 '16 at 14:06
• It looks to me like the 9th number is "23". (Or is that the 11th one? Counting is hard!) Dec 7 '16 at 17:01

The next numbers in the sequence are:

73, 101, 104, 103
The lowest numbers that have $n$ characters when written out, $n$ starting from $n=3$

Full list goes:

1 -> ONE
0 -> ZERO
3 -> THREE
11 -> ELEVEN
15 -> FIFTEEN
13 -> THIRTEEN
17 -> SEVENTEEN
24 -> TWENTY-FOUR
23 -> TWENTY-THREE
73 -> SEVENTY-THREE
101 -> ONE HUNDRED ONE
104 -> ONE HUNDRED FOUR
103 -> ONE HUNDRED THREE

• Hmm i see now that next to 15 missing, 7 should be 3 as well. Maybe I'm missing something myself... Dec 7 '16 at 14:11
• I don't make puzzles well at school T_T sorry
– bleh
Dec 7 '16 at 14:12
• Haha :D Nice catch @Levieux +1 Dec 7 '16 at 14:13
• These little errors did prevent anyone from looking the series up on oeis.org, though :P Dec 7 '16 at 14:19
• @Levieux It's not a bug, it's a feature :)
– Rubio
Dec 7 '16 at 16:23

One possible solution to this is:

1, 0, 7, 11, 14, 17, 24, 23, 30, 34, 37, 40, 47, 46, etc

Which is simply

Doing the sequence from 0 forward again (+7, +4, +3, +3, +7, -1, etc)

I think this may have other solutions though.