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  1. Generate arbitrarily long sequences of consecutive numbers without ...

    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 generating …

  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 be ...

    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 always be …

  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 of prime …

  6. Arrangements of a,a,a,b,b,b,c,c,c in which no three consecutive letters ...

    Sep 28, 2016 · Four pairs of consecutive identical letters: Again, we have two cases. We have two blocks of three consecutive identical letters (two sets of two overlapping pairs), or we have one block …

  7. 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, but i did …

  8. 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 consecutive positive …

  9. Sum of consecutive numbers - Mathematics Stack Exchange

    Jan 12, 2015 · Conversely, each representation of N N as a sum of consecutive natural numbers arises in this form, since it is centred either about an integer or about a half integer; in the first case the …

  10. Binary Sequences of length $n$ without $k$ consecutive $1$s or $0$s

    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 …