What number continues the sequence?
1 2 4 8 16 31 ?
Hint:
The numbers are the answers of a mathematical question.
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1 
- 3$\begingroup$ Please see Number-Sequence Puzzles: What (Not) To Do? $\endgroup$Mithical– Mithical2017-10-25 14:23:33 +00:00Commented Oct 25, 2017 at 14:23
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3 Answers
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The next number is
57
Because these are the
Maximal number of regions obtained by joining n points around a circle by straight lines
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2 The answer could be
57: the number of regions a circle is divided into by $n$ points.
or
61: the "Pentanacci" numbers, where each number is generated from adding the previous five (and numbers before the start of the sequence are 0).
or perhaps
62: the divisors of 492, the third perfect number.
or even
46: the Stoehr sequence for $h=4$.
or maybe
60: the number of binary sequences of length $n$ not containing "01110".
All of these were found with the OEIS, and they all give different answers. I assume you're looking for the first one, but the second is plausible as well.
- $\begingroup$ the second one is not a mathematical question. It is a number sequence. $\endgroup$yukashima huksay– yukashima huksay2017-10-30 14:47:28 +00:00Commented Oct 30, 2017 at 14:47
- $\begingroup$ I don't thing my sequence was a nice sequence anyway tho:D $\endgroup$yukashima huksay– yukashima huksay2017-10-30 14:47:48 +00:00Commented Oct 30, 2017 at 14:47
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These are
(maximal) numbers of regions formed by placing 1,2,... points on the circumference of a circle and joining them with straight lines. This equals $\binom{n}{0}+\binom{n}{1}+\binom{n}{2}+\binom{n}{3}+\binom{n}{4}$, which is the same as $2^n$ for $n\leq4$, but after that grows more slowly.
[EDITED because I'd slightly fluffed the description.]
answered Oct 25, 2017 at 14:18