Questions tagged [integer-sequence]
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115 questions
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Turning integer sequences into an elastic gold bracelet
I want to turn finite integer sequences, or a finite subset, into an elastic bracelet. Below I have answer for how to do this that took me a while to think of how to do. It still isn't perfect as the ...
- 687
4
votes
2
answers
162
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Partitions of an integer into sums of nonnegative integer powers of its decimal digits
Problem statement: I am trying to write a function that calculates the number of distinct ways an integer can be expressed as a sum of nonnegative integer powers of its decimal digits and return this ...
- 347
1
vote
2
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227
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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
3
votes
2
answers
297
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Count the longest streak output
Given a number, I am trying to find the longest streak of positive divisibility into sequential smaller numbers. Here's an example:
We have this 2D list:
...
- 1,747
2
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1
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147
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How to find a closed form for this pattern (if it exists)?
Suppose we have the following code:
...
- 81
0
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1
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156
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2
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2
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166
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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 ...
- 7,681
20
votes
6
answers
1k
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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
...
- 84.8k
5
votes
4
answers
283
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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
answers
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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
votes
1
answer
151
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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
0
votes
1
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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
votes
1
answer
423
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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
1
vote
1
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Nested sequence evaluation seems to fail [closed]
I tried do define two OIES Sequences like that:
...
