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 …
Minimum size of a sequence summing to $2013$ that guarantees a ...
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
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 …
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 ...
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 …
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?
statistics - Probability of at least X consecutive failures over N ...
Apr 30, 2017 · To summarize, it is the probability of seeing at least (X) consecutive losing trades within a 50-trade period, given a list of defined winning percentages. I want the formula/model to solve this so …
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 …
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)$.
How do I prove that for every positive integer $n$, there exist $n ...
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 ...