General term of $1,2,3,10,11,12,13, \dots$ what is the 444th term of the series $1,2,3,10,11,12,13,20,21,22,23,30,31, \dots$
 A: First of all, this is a sequence not a series.
Ok, so how about this...
01,02,03,10,
11,12,13,20,
21,22,23,30,
31,…
Can you see the pattern? :)
If you do observe the pattern, the 444 term would be 1110
A: Based on comments on other answers, you may have guessed that the given information does not determine a unique answer.  As to a hint at what the commenters might be thinking (which would also be my first guess), a number like 12571 is normally taken to mean $1\cdot 10^4+2\cdot 10^3+5\cdot 10^2+7\cdot 10^1+1\cdot 10^0$—that is, we normally interpret strings of digits to be in "base 10" where the digits read from the right represent coefficients of successively higher powers of 10.  In base 10, we use digits 0-9.  Your sequence only uses digits 0-3.  Supposing that your sequence were not in base 10, what would this suggest?
A: What do you think the next 10 terms are? Then how can you express the nth term in terms of n/4 and n mod 4?
A: By observation, the $n$th term in the sequence may be given by $10\lfloor\frac{n}{4}\rfloor +k$ where $k$ is the remainder when $n$ is divided by $4$ and $\lfloor x\rfloor$ denotes the largest integer not larger than $x$. Since $444$ is a multiple of $4$, the $444$th term is simply $1110$.
A: 12330 since 444 is 1$\times4^4+$ 2 $\times4^3+$ 3 $\times4^2+$ 3 $\times4+$ 0 $\times1$.
