Questions tagged [integer-sequence]
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112 questions
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Table takes too long to generate a recursive sequence
Here is, I think, a relatively simple code to generate a recursive sequence, but it takes Mathematica forever to generate those tables. I can understand maybe why it takes so long to generate the ...
- 11
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1
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114
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How to find a closed form for this pattern (if it exists)?
Suppose we have the following code:
...
- 151
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126
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2
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2
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144
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Recovering formulas for sequences with integer coefficients
Suppose I know the sequence is of the $a n^4 + b n^3 + c n^2 + d n$, with positive integers $a,b,c,d$, what is the easiest way to get them from the first few coefficients?
Here are the sequences I'm ...
- 6,953
20
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6
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970
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Peaks, plateaus and ledges
I want to find the peaks, plateaus and ledges of an integer sequence, but all my attempts failed.
1. Example list
...
- 83.7k
5
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4
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210
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Joining constant arrays determined by a subsequence of contiguous block of ones
I have the following:
data = {15, 25, 35, 45, 55, 65, 75, 85, 95, 105};
selector = {0, 1, 1, 0, 1, 1, 1, 0, 0, 0};
I want to create the following list from ...
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8
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How can I define a sequence of Integers which only contains the first k integers, then doesn't contain the next j integers, and so on
I need a list of integers to check if a variable has one of the values of the list.
If[ MemberQ[List,x], Green, Red]
The list contains integers and is characterized ...
- 446
3
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1
answer
122
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Enumeration of a certain sequence IV
Let $F_n$ denote the $n$-th Fibonacci number. I am interested in the sequence $$a(k, n)=\left | \left \{0 \leq m \leq n: \frac{F_m}{k} \; \text{is a perfect square} \right \} \right |,$$
where $|\...
- 105
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Derivative with respect to a sequence
I want D[Subscript[a, k],Subscript[a,j]] to return something like the Kronecker delta. Is this possible?
-1
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4
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How to prove that 3(x) + y always results in a triangular number? [closed]
Assume that :
x = (n^2-n)/2
y = ((n+1)^2)-(n+1))/2
n is an integer and n ≥ 0
Examples =
3(0) + 1 = 1
3(1) + 3 = 6
3(3) + 6 = 15
and so on.
- 9
8
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1
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314
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Recurrences related to Ramanujan's 1/pi formulas for level 10?
In the course of my research years ago, I came across three integer sequences related to Ramanujan's pi formulas but for level $10$. Their recurrence relations may be important. (Just like the level $...
- 457
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Nested sequence evaluation seems to fail [closed]
I tried do define two OIES Sequences like that:
...
5
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1
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424
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Writing a number 'm' as a sum of 'n' prime numbers
We can write {2 = 2}, {3 = 2+1, 3 = 3}, {4 = 2+2, 4 = 3+1}, {5 = 3+2, 5 = 2+2+1}, {6 = 3+3, 6 = 5+1, 6 = 3+2+1} and so on. I am trying to write every positive integer as a sum of Prime numbers.
In ...
- 145
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6
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372
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Subsequences with distinct values
(this question was modified after initial answers)
For a sequence
x = {6,4,2,4,2,4,6}
y = Subsequences[x]
gives the list of ...
- 515
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0
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Calculate an n-order determinant by FindSequenceFunction
Calculate an n-order determinant:
$\left|\begin{array}{cccccc}1 & 2 & 3 & \cdots & n-1 & n \\ n & 1 & 2 & \cdots & n-2 & n-1 \\ n-1 & n & 1 & \cdots ...
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