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 and …

May 16, 2016 · The sum of $a$ consecutive odd numbers is a difference of squares $ (n + a)^2 - n^2 = a (a + 2n)$.

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 of prime …

Jan 12, 2021 · @Baropryl In both of your examples, you construct your consecutive numbers such that the smaller of the two is the even number. You must explicitly consider the case that the smaller of …

Mar 6, 2023 · Closed 2 years ago. 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 …

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 days ago

Jan 12, 2015 · Sum of consecutive numbers Ask Question Asked 10 years, 10 months ago Modified 2 years, 8 months ago

Basically, on average, how many times one should roll to expect two consecutive sixes?

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, however, …

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, but i did …