Consecutive composite numbers - Mathematics Stack Exchange
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, …
Longest known sequence of identical consecutive Collatz …
Aug 19, 2013 · I have found a sequence of 67,108,863 consecutive numbers that all have the same Collatz length (height). These numbers are in the range $ [2^ {1812}+1, 2^ {1812}+2^ …
Generate arbitrarily long sequences of consecutive numbers …
Aug 25, 2022 · Question Can those hidden consecutive points have a prime coordinate? If true, then this idea isn't valid. If false (hurray!), is it possible to simplify the Theorem to focus on …
The product of $n$ consecutive integers is divisible by $n$ factorial
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 …
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?
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 …
Confirming a easy proof: the product of two consecutive numbers …
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 …
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, 1 month ago Modified 11 years, 9 months ago
Probability - consecutive numbers - Mathematics Stack Exchange
Sep 4, 2015 · Question: Three numbers are selected out of the first 30 natural numbers. What is the probability that none of them are consecutive? I know that the total possibilities will be …
algebra precalculus - Proving the product of four consecutive …
Jun 27, 2018 · Assume $m$ is the product of four consecutive integers. If $m$ is the product of four consecutive integers, then write $m=x (x+1) (x+2) (x+3)$ where $x$ is an integer.