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Questions tagged [integer-sequence]

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Accessing internal calculations of Mathematica code

For a given Mathematica program that generates a sequence x of integers, is it possible to also generate equal length sequences of integers that were used internally by the Mathematica kernel to ...
177 views

solve for two variables for each n related to Collatz conjecture

For this code, for each x I would like to solve for all value ranges for c1 and c2 in a bounded range ie c1 and c2 in the range of real numbers +-100 for c1 and c2 for each x, which combined give "...
178 views

Finding recurrence formulas from procedural code and output lists associated with integer sequences

This code outputs 37 sequences and takes about 15-minutes to run. I would like to be able to see how many and which variables { i, j, k, m, n } each of the 37 ...
298 views

Return last number in sub-sequences in a list of integers

Given a list of integers like this: z = {113, 117, 118, 119, 120, 121, 475, 476, 529, 538, 542, 543, 544} I want a function that returns: ...
101 views

Integer sequence and RAM limits

I am trying to calculate the set of unique differences in a sequence, however the sequence grows fast and I hit the RAM limit of my PC for nthPrimeToUse = 11. For nthPrimeToUse 1 to 10 the output of ...
953 views

Generate and graph the Recamán Sequence

I was surprised to see that we don't have any posts that mention the Recamán Sequence, so I figured I should post it as a challenge. By definition, $a_0=0$ and $a_n=a_{n-1}-n$ if the r.h.s. is ...
840 views

RandomInteger with equal number of 1 and -1

I want to generate a list of random integers with only three values 1,0,-1. I know it can be done through RandomInteger[{-1, 1}, n]. How can I impose constraint on this list so that every integers in ...
96 views

Mathematica analog to Wolfram|Alpha dataset analysis [closed]

I have a set of sequences with length 8,48,480,5760,.. and would like to do sequence analysis on them. I plugged the length 8 sequence into wolframalpha: https://www.wolframalpha.com/input/?i=11,+2,+...
34 views

Find all integer tuples in a bounded region

For given rational numbers $p_1/q_1,p_2/q_2,p_3/q_3$ and a negative integer $d$, I'd like to find quadruples of integers $(w,x,y,z)$ in a rectangle(of particular sidelengths) satisfying the series of ...
62 views

FindGeneratingFunction gives up too easily [closed]

I am trying to automatically find a generating function from the coefficients of a simple rational function using Mathematica's FindGeneratingFunction: ...
133 views

Constructing the following figure using mathematica

How do I construct the figure in the image using the formulae in Mathematica? I defined the following functions for the 4 cases. Can you also explain the significance of these in relation to the ...
740 views

How to construct rectangular figures from the Fibonacci numbers?

How do you construct rectangular figures ("golden rectangles") using the Fibonacci numbers in Mathematica using graphics? I know that the basis of the construction of these figures are the formulae ...
66 views

How to postulate a formula for the following Mathematica function

I am using Mathematica to explore the properties of the Fibonacci Sequence. Below is the functions I have defined ...
84 views

how to obtain these increasing integers for given n and m?

Let n and m be natural numbers. Then, how does one write a function ordint[n,m] that gives ...
98 views

Guess Diophantine equation from its solutions

Take for example the equation $$n^2=x^2+y^2+1$$ where $x,y$ are integers. This equation admits solutions only for some values of $n$, to wit, $$n=1,3,9,17,19,33,35,51,73,81,99,\dots$$ Can we ...