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# Questions tagged [integer]

For challenges involving the manipulation of integers.

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### Print the Lost numbers

As a big fan of the Lost TV series, I always got intrigued by the sequence of numbers that repetitively appears on the episodes. These numbers are: $4, 8, 15, 16, 23, 42$ (A104101) Using any ...
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### The inverse Collatz Conjecture

I think the Collatz Conjecture is already well-known. But what if we invert the rules? Start with an integer n >= 1. Repeat the following steps: If n is even, multiply it by 3 and add 1. If n is ...
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### New Neighbour Sequence

The non-negative integers are bored of always having the same two* neighbours, so they decide to mix things up a little. However, they are also lazy and want to stay as close as possible to their ...
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### The Written Digits Sequence

Here's a reasonably trivial sequence which is not in the Online Encyclopedia of Integer Sequences. Start with an empty sequence then define each term as the number of characters required to write out,...
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### Multiplicative undelta

Let us define the "multiplicative deltas" of values $[\; a_0, \cdots a_N, \;]$ as: $$[\; a_1 / a_0, \cdots, a_{i+1} / a_i, \cdots, a_N / a_{N-1} \;]$$ The reverse operation - namely "...
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### Length of a UTF-8 byte sequence

Determine the length of a UTF-8 byte sequence given its first byte. The following table shows which ranges map to each possible length: ...
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### Every positive integer can be written as the sum of 3 palindrome integers. Wha'ts the largest possible palindrome integer for each integer n? [duplicate]

Let n be a positive integer then n = a + b + c for some a, b, and c that are palindrome integers. What is the largest possible integer ...
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### Longest Repeating Subsequence of a Single Digit

Challenge: Given a positive integer, output the longest single-digit subsequence that occurs at least twice, AND has boundaries of another digit (or the start/end of the integer). An example: Input:...
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### Whose neighbours are hostile?

Introduction For the purposes of this challenge, we will define the neighbours of an element $E$ in a square matrix $A$ (such that $E=A_{i,j}$) as all the entries of $A$ that are immediately ...
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### Replace me by the sum of my cyclic successors!

I have a simple challenge for you this time. Given an array of positive integers A (or the equivalent in your language), replace each entry Ai with the sum of the next Ai elements of A, cycling back ...
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### Classify a region by its slope

Definitions The kth ring of a square matrix of size N, where 1 ≤ k ≤ ceiling(N/2) is the list formed by the elements of the kth and (N-k+1)th rows and columns, but without the first and last k-1 ...
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### X Steps Forward, 1 Step Back

Here the first 100 numbers of an easy sequence: ...
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### Up and down, up and down

Challenge: Given a positive integer input n, create a vector that follows this pattern: 0 1 0 -1 -2 -1 0 1 2 3 2 1 0 -1 -2 -3 -4 -3 -2 -1 ... ±(n-1) ±n ...
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### Make Three from One [duplicate]

Given a single digit integer and a three digit integer, output a mathematical formula that uses only the single digit and a given list of operators to equal the three digit integer. Input: A one ...
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This challenge is related to some of the MATL language's features, as part of the May 2018 Language of the Month event. Introduction In MATL, many two-input functions work element-wise with ...
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### Knight Distance

In Chess, a Knight on grid (x, y) may move to (x-2, y-1), (x-2, y+1), (x-1, y-2), (x-1, y+2), (x+1, y-2), (x+1, y+2), (x+2, y-1), (x+2, y+1) in one step. Imagine an infinite chessboard with only a ...
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### Generate lowest degree polynomial from sequence [duplicate]

Introduction A sequence of numbers is passed in as the input. The program has to generate the lowest degree polynomial possible. This was my first programming project in college and it would be ...
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### Arithmetic Cycle

Input: Integer n which is >=0 or >=1 (f(0) is ...
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### Digit Occurrences

Input: A list of integers (which will never contain a zero) Output: A list of the same size with counts based on the following: If the current item is negative: Look at all items before this item, ...
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### Interval Notations

Challenge: Input: Two integer parameters a and b (where a<b and the difference is at ...
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### Not Quite Roman Ternary

Given an integer n ≥ 0 , output it in a non-positional base-3 notation, using digits 139ABCDE… and a 1-character separator. Every digit is a consecutive power of 3 ...
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### Digits in their lanes

Input: A list of integers Output: Put each digit (and the minus sign) in its own lane, in the order -0123456789, ignoring any duplicated digits. Example: Input:...
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### Which Card is it?

Introduction Long ago, when I used to code card games with usual playing cards, I used to specify a number for each card and call a function with some number to get a card. This somewhat inspired me ...
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### Is this a truncated triangular number?

Related OEIS sequence: A008867 Truncated triangular number A common property of triangular numbers is that they can be arranged in a triangle. For instance, take 21 and arrange into a triangle of <...
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### Crazy but Rational Bases

We have many challenges based on base 10, base 2, base 36, or even base -10, but what about all the other rational bases? Task Given an integer in base 10 and a rational base, return the integer in ...
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tl;dr: Output the values where the reduced prime factorization leader changes. Every positive integer has a unique prime factorization. Let's call the reduced prime factorization just the list of ...
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### Make Zero From First 'n' Numbers

Challenge The challenge is to write a code that takes a positive integer 'n' as an input and displays all the possible ways in which the numbers from 1 - n can be written, with either positive or ...
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### Find The Local Maxima And Minima

Definition The maxima and minima of a given function are the largest and smallest values of the function either within a given range or otherwise within the entire domain of the function. Challenge ...
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### Can square tree rings be generated from primes?

Apparently yes! In three easy steps. Step 1 Let f(n) denote the prime-counting function (number of primes less than or equal to n). Define the integer sequence s(n) as follows. For each positive ...
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### Find number of ones to get a number using + and *

Introduction Your goal is to find the least number of ones you need to add or multiply together to get the input value, this is A005245. Input One positive integer N. Output The smallest number ...
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### Bottom part of the Hourglass

Challenge: Input: Three integers: bottom-edge length; starting amount of grains of sand; index Output: Output the state of the bottom part of an hourglass at the given index, based on the given ...