# Are Mjaavatten

Retired physicist with background in the petroleum and process industry. My main interests are mathematical modelling, numerical methods, and thermodynamics.

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Solved

Easy Sequences 40: Quadratic Congruence

Quadratic Congruence is a modular equation of the form: . In this exercise you will be given a vector containing the coefficie...

8 days ago

Solved

Compute the largest number whose prime factors sum to n

This problem deals with a sequence whose tenth term is 36 because the prime factors of 36 (2, 2, 3, 3) sum to 10. The number 32 ...

9 days ago

Solved

Easy Sequences 38: Prime Number Delta

The Prime Number Theorem states that: where is the prime counting function (number of pri...

9 days ago

Solved

Easy Sequences 30: Nearly Pythagorean Triangles

A Nearly Pythagorean Triangle (abbreviated as "NPT'), is an integer-sided triangle whose square of the longest side, which we wi...

19 days ago

Solved

Easy Sequences 33: Web Trapped Ant

An ant is trapped on a spider web inside a can with open top. The can has a radius and height . A spider sitting on the outside...

21 days ago

Solved

Easy Sequences 24: Number of Coprime Lattice Points

Given a number 'n', you were tasked to mark and count all coprime lattice points at the first quadrant bounded by the points (0,...

24 days ago

Solved

Easy Sequences 22: Sum of Proper Fractions

Let 'F' be the set of all proper fractions in lowest term, whose denominator is less than or equal 'd'. So, for d = 10, we have:...

27 days ago

Solved

Easy Sequences 26: Prime-Integer Line Segments

At the first quadrant in the -plane, you are asked to construct a line segment with the following specifications: Select a prim...

27 days ago

Solved

Magic is simple (for beginners)

Determine for a magic square of order n, the magic sum m. For example m=15 for a magic square of order 3.

1 month ago

Solved

Make a logical diamond using GALLERY function

Inspired from <http://www.mathworks.com/matlabcentral/cody/problems/1078-make-a-diamond Problem 1078. Make a diamond> In thi...

1 month ago

Solved

The Piggy Bank Problem

Given a cylindrical piggy bank with radius g and height y, return the bank's volume. [ g is first input argument.] Bonus though...

1 month ago

Solved

Make a diamond

Given n, odd number > 1, return n by n matrix consist of "null" and "*" characters arranged like a diamond. No toolbox funct...

1 month ago

Solved

Special matrix

Make a square matrix with this shape. For n=4 M = 1 1 0 0 1 0 1 0 0 1 0 ...

1 month ago

Solved

Create Volcano (or Atoll) martix. It is an extension of Bullseye matrix problem.

For example, if n=2 (maximum value), the output matrix should be [1 1 1 1 1; 1 2 2 2 1; 1 2 1 2 1; 1 2 2 2 1; 1 1 ...

1 month ago

Solved

Mirror Image matrix across anti-diagonal

Given an input number x, create a mirror image matrix 'Y' across the anti-diagonal. For example, if x=3, Y = [1 2 3; ...

1 month ago

Solved

Pascal's Matrix

Given an integer n ≥ 0, generate the ( _n_+1) × ( _n_+1) lower triangular <http://en.wikipedia.org/wiki/Pascal_matrix P...

1 month ago

Solved

Easy Sequences 20: Counting Prime-sided Rectangles

A prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-...

1 month ago

Solved

Easy Sequences 11: Factorial Digits without Trailing Zeros

Here is an easy one... It is not difficult to count the number of digits of the factorial of a given number. For example for 'n...

1 month ago

Solved

Easy Sequences 19: Length of Prime-sided Rectangle with Maximum Area

A prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-...

1 month ago

Solved

Construct a prime circle

A <https://mathworld.wolfram.com/PrimeCircle.html prime circle> is a circular arrangement of the numbers 1 to 2n such that pairs...

1 month ago

Solved

Multiply binary numbers

Write a function to multiply two binary numbers input as strings. For example, input values of ‘1011’ and ‘101’ should give ’110...

1 month ago

Solved

List the Moran numbers

The quotient of a Moran number and its digit sum is prime. For example, 117 and 481 are Moran numbers because 117/(1+1+7) is 13 ...

1 month ago

Solved

Pi Digit Probability

Assume that the next digit of pi constant is determined by the historical digit distribution. What is the probability of next di...

1 month ago

Solved

Easy Sequences 13: Average Speed of Spaceship

A certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ...

1 month ago

Solved

Identify Wagstaff primes

The numbers 3, 43, and 2731 are examples of <https://mathworld.wolfram.com/WagstaffPrime.html Wagstaff primes>. Write a func...

1 month ago

Solved

Count the primes in Collatz sequences

Several Cody problems (21, 69, 42937, 44448, 44784, 52422) involve Collatz sequences. These start with a seed . If is odd, the ...

1 month ago

Solved

Easy Sequences 12: 50th Prime

Write a function that outputs the 50th prime after a given number. For example, the 50th prime after 500 is 829. NOTE: If 'n' i...

2 months ago

Solved

Easy Sequences 1: Find the index of an element

The nth element of a series A is defined by: . Obviously, the first element A(1) = 1. Given the nth element 'A(n)', find the val...

2 months ago

Solved

Easy Sequences 2: Trigonometric function with integral input and output

The function 'F', defined as: , will always return an integer if the input is a natural number (in radian...

2 months ago

Solved

Easy Sequences 9: Faithful Pairs

A "faithful number" is a non-prime number that is one less or one more than some prime number but not both. For example, for num...

2 months ago