Generate arbitrarily long sequences of consecutive numbers …
Aug 25, 2022 · The goal of this question is to find if other methods exist to generate arbitrarily long sequences of consecutive numbers without primes. I started searching for other formulas …
Minimum size of a sequence summing to $2013$ that guarantees …
Nov 25, 2025 · Minimum size of a sequence summing to $2013$ that guarantees a consecutive subset sum of $31$ (still wanted rigorous proof) Ask Question Asked 11 days ago Modified 9 …
Sum of consecutive odd numbers - Mathematics Stack Exchange
May 16, 2016 · The sum of $a$ consecutive odd numbers is a difference of squares $ (n + a)^2 - n^2 = a (a + 2n)$.
I'm trying to find the longest consecutive set of composite numbers
Jun 6, 2017 · In terms of this structure, the composite topologies representing the composite region in the k-tuple ensure that the frontier prime elements are consecutive in the sequence …
Prove the product of 3 consecutive positive integers is always ...
Mar 6, 2023 · There is a problem asking me to prove the product of 3 consecutive integers is always divisible by 6 by using induction and not using the fact that one of the 3 numbers must …
probability - What is the expected number of times a dice has to …
Basically, on average, how many times one should roll to expect two consecutive sixes?
The difference of two consecutive perfect squares is always odd
Since they are consecutive, one is even and the other is odd. Now, squaring the even number is multiplying it an even number of times, so the answer is even. Squaring the odd number, …
Why are the differences between consecutive squares equal to the ...
Then you get 9 which is the next cosecutive square, (3^2). That is the concept of the equation above, technically i didn`t explain that specific aspect of the difference of consecutive squares, …
Proof: Sequence of n consecutive natural numbers containing no …
Proof: Sequence of n consecutive natural numbers containing no primes (Velleman P158 Thm 3.7.3) Ask Question Asked 12 years, 2 months ago Modified 11 years, 10 months ago
Prove every odd integer is the difference of two squares
Dec 21, 2012 · Eric and orlandpm already showed how this works for consecutive squares, so this is just to show how you can arrive at that conclusion just using the equations.