Find a pattern for the following sequence. 1,1,3,1,3,5,7,1,3,5,7….. Let n= the nth number. Find the nth number of this series

This is maybe more of a question for matheducators.SE than math.SE but I’m more interested in the math than the education. A common problem given to middle and high school kids (at least in America) is something like “Find the next number in the sequence $2,4,8,16,\dots$”. Now I am not against this problem, finding patterns […]

What is the largest number on multiplying with itself gives the same number as last digits of the product? i.e., $(376 \times 376) = 141376$ i.e., $(25\times 25) = 625$ If the largest number cant be found out can you prove that there is always a number greater than any given number? (only in base […]

I have a homework. It seems to be an easy sequence but I can’t get the answer. So, What is the next element? $$2, 7, 10, 13, 23, 34,?$$ What would be the solution out of these numbers? 45 or 49 or 58 or 39

While working on a problem, I came to this: What is the $n$th derivative of the hyperbolic cotangent? For simplicity, let $c=\coth(x)$. $c^{(0)}=c$ $c^{(1)}=-c^2+1$ $c^{(2)}=2c^3-2c$ $c^{(3)}=-6c^4+5c^2-2$ $c^{(4)}=24c^5-34c^3+10c$ Etc. It appears to be representable as a polynomial of $c$. Any ideas on what the coefficients are? Update: It appears the leading coefficient is trivially given by […]

I saw this pattern of binary numbers with constraints first number should be 1 , and two 1’s cannot be side by side. Now as an example 1 = 1 10 = 1 100,101 = 2 1000,1001,1010 = 3 10000,10001, 10010, 10100, 10101 = 5 Strangely I see the numbers we can form of this […]

I have been working on an article at https://oeis.org/wiki/Table_of_convergents_constants where I posted a table of “convergents constants” (defined at https://oeis.org/wiki/Convergents_constant) for a few numbers. It would be nice to support the article with some quality analysis. Before June 9, 2011, was starting to extract and clearly define a pattern to these constants cf the article. […]

In a stack of n distinct cards in order {1,2,3,4,…,n} from top, define distance between 2 cards as the number of cards between them. 2 cards are neighbours if they’re adjacent in original stack, if their index differs by 1. How many card rearrangements (permutations) satisfy the following? I) The sum of distances between any […]

I have been stuck in finding the general term and the sum of $n$ terms of the series $$12,\,40,\,90,\,168,\,280,\,432, …$$ I am not able to see any relationship between the successive terms of the series. Is there a pattern which I am not able to see?

Consider the sequence: $$a_0=x,~~~b_0=y$$ $$a_{n+1}=\frac{1}{2} \left(a_n+\sqrt{\frac{a_n^2+b_n^2}{2}} \right),~b_{n+1}=\frac{1}{2} \left(b_n+\sqrt{\frac{a_n^2+b_n^2}{2}}\right)$$ $$\lim_{n \to \infty} a_n=\lim_{n \to \infty} b_n=l(x,y)$$ I can’t pin down the pattern for the limit. Numerically, I’ve got the following result: $$\frac{1}{l(x,y)}=\arctan (f(x,y))$$ What is the explicit expression for $f(x,y)$? Numerical examples: $$\begin{array}( x & y & \frac{1}{l(x,y)} \\ 1 & 2 & \arctan \left( \frac{3}{4} […]

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