Reputation
23,416
Top tag
Next privilege 25,000 Rep.
Access to site analytics
Badges
2 31 64
Newest
 Revival
Impact
~402k people reached

9h
comment Queue automaton algorithm for accepting primes
Use a representation like '1aaaa2aaa' to hold two numbers at once (the number of $a$'s after the $1$ and after the $2$); call them $x_1$ and $x_2$. Think of how to do the following three things (using additional pointer symbols): check whether $x_2 \ge x_1$, check whether $x_2$ divides $x_1$, and increment $x_2$. Then initialize with $x_2=2$ and check divisibility and increment until either $x_2$ divides $x_1$ (not prime) or $x_2 \ge x_1$ (prime).
Feb
5
awarded  Revival
Feb
3
answered Logic - Is it safe to state the following?
Feb
1
answered How to compute the chances of wining on this game?
Jan
27
answered Density of numbers with exactly $n$ distinct prime factors in $\mathbb{N}$
Jan
25
comment Which function to kill: Sine or Cos?
For linear second-order differential equations, you'll have two independent coefficients that need to be determined by the initial conditions (e.g., by $V(0)$ and $V'(0)$).
Jan
21
comment $96$ balls in $4$ boxes
There are only four arrangements where all $24$ red balls are together... do you see why? Next, can you calculate the total number of possible arrangements, $N$? In which case the probability is $4/N$.
Jan
20
comment Mathematics notations
It means the set $\{1,2,3,\ldots,n\}$.
Jan
19
answered Optimal Strategy for this schoolyard game - (Charge, block, shoot)
Jan
15
comment Brown Bears Bidding on Honey
Assuming not (i.e., no collusion), the dominant strategy may well be for each bear to bid his true value, as in the Vickrey auction. I think you should clarify (if it's correct) that the payoff to the winning bear is $v_i$ minus the amount paid, not $v_i$ minus the amount bid.
Jan
15
comment Brown Bears Bidding on Honey
Do the bears know what values the other bears place on the honey?
Jan
14
answered The $n$th prime number is $85489307341$. How to find $n$?
Jan
14
answered Use an induction argument to prove that for any natural number $n$, the interval $(n,n+1)$ does not contain any natural number.
Jan
13
comment How can I recover a sequence of numbers given a corrupted version of it?
Are the numbers in the sequence related to each other, i.e., is it some kind of time series? In which case approaches like the Kalman filter are standard.
Jan
13
comment Paradox: Summation of natural logarithms
This phenomenon has nothing to do with logarithms and can be exhibited much more simply as follows: consider $\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdots$. Everything but the $2$ cancels, so the result should be $2$... but every term in the product is less than $1$, so the result must also be less than $1$!
Jan
13
answered Show $\left( \int_1^e f(x) \; dx \right)^2 \leq \int_1^e x\,f(x)^2 \; dx$
Jan
13
comment On Digts of Cubes and Squares
This hand-wavy argument gets it about right. I find one example for $i=1$ ($69$), one for $i=2$ ($6534$), $10$ examples for $i=3$ ($497375$, $539019$, etc.), and $270$ examples for $i=4$.... the approximation derived above underestimates the number of examples by about a factor of three.
Jan
9
awarded  Yearling
Jan
7
comment Why does step size in fourth order runge-kutta methods less than 1?
There's nothing magical about $1$; it just depends on the scale over which your function varies. The coefficients of the error terms will depend on the derivatives of the solution; that's what will really determine how small $h$ needs to be.
Jan
7
comment Abelian Matrices
It might be interesting for you to consider the conditions on a set of matrices needed for any two matrices in the set to commute with each other. For instance, a set containing the identity matrix and (any) one other matrix has this property. Are there larger sets that work?