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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Are there infinitely many "super-palindromes"?

Let me first explain what I call a "super-palindrome": Consider the number $99999999$. That number is obviously a palindrome. ${}{}{}{}$ The largest prime factor of $99999999$ is $137$. If you divide $99999999$ by $137$, you get $729927$. This…
celtschk
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Pattern "inside" prime numbers

Update $(2020)$ I've observed a possible characterization and a possible parametrization of the pattern, and I've additionally rewritten the entire post with more details and better definitions. It remains to prove the observed possible…
Vepir
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Can a number be a palindrome in 4 consecutive number bases?

Edit $(2020)$: Update is included at the end of the post. $4$ consecutive bases? Are there numbers that are a palindrome in $4$ consecutive number bases? I'm not counting a one digit palindrome as a palindrome. (Discarding trivial…
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Do all natural numbers have a nonzero multiple that is a palindrome in base 10?

Some natural numbers have a nonzero multiple that is a palindrome in base 10. For example, $106 \times 2 = 212$, which is a palindrome, and $29 \times 8 = 232$, which is also a palindrome. Aside from 0 (which only has 0 as a multiple), are there…
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Structures emerging in a discrete plot of palindromic numbers

Plotting Palindromic Numbers & Number Systems If we decide to plot Palindromic Numbers against Number Bases, and go far enough into the number line, things start to look interesting. In fact, the deeper we go into the number line, we get similar…
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Question about a program generating palindromic prime numbers

I'm a programmer and software designer. I'm definitely not a mathematician and my maths is quite basic. One of my colleagues challenged me to generate a palindromic prime number, at least 1000 digits long and using only the digits 1 and 7. I wrote a…
gd1
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Average Length of Longest Palindromic Subsequence

Suppose there is a finite set $A$ containing $n$ elements. One can construct a sequence of finite length: $$\{a_i\},\ a_i \in A,\ i\in \mathbb N,\ i\le N$$ This sequence contains $2^N$ subsequences of the form: $$\{ a_{i_k}\}, k\in \mathbb N,\…
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Decimal/hex palindromes: why multiples of 53?

A previous question 371 = 0x173 (Decimal/hexidecimal palindromes?) described numbers whose decimal and hex representations are reversed of each other. Other than the trivial one-digit numbers, there are only $5$ numbers with this property. My…
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Why are there palindromic subsequences at random among this sequence?

So I was thinking about the Goldbach conjecture and I rephrased it to myself as the following: Prove that every number N is either prime or else lies halfway between two primes A and B, where A < N and N < B < 2N. This is equivalent, because if it…
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Is 2201 really the only non-palindromic number whose cube is palindromic?

Hі, Wikipedia states that 2201 is the "only known non-palindromic number whose cube is palindromic", and lists no reference. It is in fact true that $2201^3=10662526601$, which is a palindrome. But to say there isn't any other number with this…
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Hard system in integers related to natural number representations

Update: Observing a necessary condition, and "unbalanced" variation A necessary (but not sufficient) condition for a number to be a solution to this Diophantine system (Representing "balanced" triple palindromes) presented in the "The…
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Finitely many palindromes in two consecutive number bases, for fixed and distinct numbers of digits

Double palindrome: ...is a number nontrivially palindromic in two consecutive bases $b,b\pm1$ Let $d_1,d_2$ be numbers of digits in the two bases: nontrivially means $d_1,d_2\gt 1$. Let $d=\max\{d_1,d_2\}$ be called the degree of a double…
Vepir
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Which number base contains the most Palindromic Numbers?

Plotting Palindromic Numbers I made a script that checks numbers through number bases and plots a black pixel if the number is a palindrome in the corresponding base. If we check the first $256$ numbers (width) and first $256$ number bases…
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Arranging a set of strings to form a palindrome: NP complete?

Is it NP complete to determine if a given set of strings can be arranged to form a palindrome? Example: The strings {"German" "man" "am" "am" "I" "I" "regal" "a"} can be arranged into "I man am regal a German am I". The strings {"bat" "bat"} cannot…
user253970
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Palindromes in multiple bases

I noticed when listing out palindromes in bases $2$ and $3$ that they seem not to share any palindromes (other than trivial single-digit palindromes). However, when I tried to prove this, I couldn't solve it. I proved it for numbers with an even…
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