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Questions tagged [palindrome]

A palindrome is a number or any other sequence of characters which remains the same when it is reversed (read backwards). Questions involving palindromes, or mathematics related to them such as the Lychrel process or Scheherazade numbers.

A palindrome is a number or any other sequence of characters which remains the same when it is reversed (read backwards).

Usually we talk about palindromic numbers (numeral palindromes) as positive integers that remain the same when their digits are reversed. As such, palindromes are dependent on the they are observed in.

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Why do palindromes form these arcs?

I was watching 3Blue1Brown's YouTube video "Why do prime numbers make these spirals?", and it inspired me to look for some patterns myself. So I made some Python code as follows below. How it works is that each nonnegative integer is placed along a…
Lemma
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Even number not the sum of two base $2$ palindromes

What's the least positive even number not a sum of two base $2$ palindromes? I've checked and it must be over $100$ since all up to $100$ are such sums. [Or, which to me seems unlikely, are all even numbers such sums?] Base $2$ palindromes entry…
coffeemath
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Project Euler exercise 4: largest palindrome made from the product of two 3-digit numbers

Consider the 4th problem of the Project Euler: A palindromic number reads the same both ways. The largest palindrome made from the product of two $2$-digit numbers is $9009$ = $91 \times 99$. Find the largest palindrome made from the product of two…
Francesco Boi
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How to make a palindromic table where each row and column is a palindrome?

I have a set of digits. For example, 3 1s, 2 2s, 10 3s, ... With this available digits how do I create a palindromic table of fixed (nxm) matrix where each row and column is palindromic? For a linear structure, I can simply do mirror reflection to…
user3243499
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Square of palindromic number

The other day I thought of this question: Is it possible to find a set of palindromic numbers such that the square of them is itself palindromic? In other words: $A = \{a : a^{2}=b$ where a,b are palindromic integers} I'm not a mathematician so I…
Davide M
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Is "aa" an even or odd palindrome?

I came across a question with a solution that says this: The context-free grammar (CFG) for palindromes of even length was given: Σ = {a, b}, P → a P a | b P b | ε Give a context-free grammar (CFG) for palindromes that allows odd-length…
just coding
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Count of palindrome numbers in the range [a,b]

Can we find the count of palindrome numbers in the range [a,b] by directly using a formula. for eg in range [8,12] there are 3 palindrome numbers (8, 9, 11)
ppSpp
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Why are multiples of 11 palindromes?

One thing I noticed is that for any integer $-10
DonielF
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How to get palindrome of a number with specific base

I have problem while reversing and checking palindrome for a number of specific base (other than 10). For example:- let's take 87. The Palindrome number is found as follows: 87+78= 165+ 561 = 726 + 627= 1353 + 3531 = Palindrome ! This method works…
HN Learner
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palindrome number

How to find the $n$-th term of the series. 1 11 101 1001 10001 100001 1000001
srox
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nth term of the series containing one 9 then two 9 and so on

nth term of the series 9, 99, 999, 9999. Is there any formula for it? 9 99 999 9999 . . . .
srox
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