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 …

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 10 days ago Modified 8 days ago

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

When I took basic number-theory course there was this exercise to find 2000 consecutive numbers. And of course it's well known that the trick to take numbers of the form $$ (n+1)!+m, \\quad 2 \\leq ...

Oct 19, 2016 · Consider the following: Find a recurrence relation and give initial conditions for the number of bit strings of length n that do not have two consecutive 0s. I am trying to understand the …

Aug 6, 2018 · Additionally, Is it possible to have $1000$ consecutive natural numbers with exactly $12$ primes between them? I have an intuition that we have to form a recurrsive relation and solve it.

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 …

I need help proving that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite. The hint that came with the ...

How can we prove that the product of $n$ consecutive integers is divisible by $n$ factorial? Note: In this subsequent question and the comments here the OP has clarified that he seeks a proof that "does …

Aug 11, 2021 · Earlier today I saw a question about binary sequences of length $n$ that contain no $3$ consecutive $1$ s or $0$ s. I want to generalize the problem a little and count the number of …