The puzzle has already been solved but you can still try it just for fun without looking at the posted correct answer.
What is the missing number in the following sequence?:
0, 4, 10, 32, ?, 317 ...
Hint # 1:
It has nothing to do with differences between given terms such as (4-0 = 4, 10-4 = 6...). Try a different pattern.
Hint # 2:
The 10 should be a clue. We use base 10 numbers so 10 is a special number and is a key part of the pattern. There is a reason it is not 9 or 11 for example.
Hint # 3:
Don't bother with + or -, those wont help. That is, for the function part (see hint 7), F(0), F(4), F(10)... don't use + or -. Take a close look at the pattern in the 5 numbers given, and think about a function of those numbers having some pattern too.
Hint # 4:
Look carefully at the number sequence. Do you see any pattern of how they are increasing in value? I can tell you they will continue to increase.
Hint # 5:
The pattern doesn't involve any complex mathematical expression, rather, it is quite simple. Run some function on each of the 5 numbers given, and analyze the output of that function, then look for a pattern. F(0), F(4), F(10)... will all follow this pattern.
Hint # 6:
The 5th term (after 32) is a 3 digit number in the range 100..316 inclusive so 100, 101, 102... 315, 316. Take your pick, but if you randomly guess, you only have a 1 in 217 chance of getting it right. Also the correct answer, (to get the checkmark), needs an explanation but "I guessed" wont "cut" it. There is a "simple" solution (pattern) to this puzzle.
Hint # 7:
There is no conditional solution, meaning that there is no particular term in the sequence (such as the first one), that is treated differently than the rest. For example, if you found a solution that works with all terms except the 1st one (at least one person submitted an answer like that but it may have been deleted), a solution that states 0 for the first term, and some other pattern for the rest, although technically a valid solution, is not what I am looking for. My solution works for any and all terms in the sequence regardless of position (1st term, 75th term, 1000th term...). However, the pattern has a relation between the function of neighboring terms. For example, suppose we define a function called F. F(0) has a relationship with F(4) and that relationship is preserved the same way between F(4) and F(10). That is, the pattern is invariant between neighboring terms. Lets us call this relationship R. Thus we have R(0,4) = R(4,10) = R(10,32) = R(32, x) = R(x, 317)...
Hint # 8:
The even # terms (2nd, 4th, 6th...), if scaled to 1 digit before the decimal point only, (4.0, 3.2, 3.17...) will become asympototic to a certain irrational number as the term positions get higher and higher (20th, 22nd, 24th...).
I am looking for a particular answer with a particular pattern that applies to all 6 numbers (5 given plus missing one). Please give your answer as a number with an explanation why you think that is the correct answer. I guess this problem is not as simple as I thought. Good luck.