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  1. 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 …

  2. 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)$.

  3. 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?

  4. Prove the product of 3 consecutive positive integers is always ...

    Mar 6, 2023 · 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 must …

  5. 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 …

  6. Sum of Consecutive Integers - Mathematics Stack Exchange

    Feb 7, 2013 · Can you give me more realistic example . Take a number say 15000 . What steps should I follow to find the number of ways by which 1500 can be expressed as sum of …

  7. Binary Sequences of length $n$ without $k$ consecutive $1$s or …

    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 …

  8. Find all sets of consecutive natural numbers whose sum is 54.

    May 7, 2023 · It appears that you have misread the question slightly, as it requests for consecutive natural numbers, and not even numbers. Below, I'll describe the amount of …

  9. The difference of two consecutive perfect squares is always odd

    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, …

  10. Why are the differences between consecutive squares equal to the ...

    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, …