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, \\quad 2 \\leq ...
Longest known sequence of identical consecutive Collatz sequence ...
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^ {26}-1]$ and I …
Generate arbitrarily long sequences of consecutive numbers without ...
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 …
probability - What is the expected number of times a dice has to be ...
Basically, on average, how many times one should roll to expect two consecutive sixes?
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 that "does …
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 of prime …
Confirming a easy proof: the product of two consecutive numbers is ...
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 …
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
Why calculating XOR of consecutive values can be simplified?
XORing consecutive integers has an interesting property. Does anyone know why? (2 answers) Closed 9 years ago. I was trying to calculate integer xor of 0..n. I named the function xored (n). Note that in …
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 $^{30}C_3$ …