Questions tagged [palindromes]
A sequence is a palindrome if it is the same when read from backward.
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Which numbers are the sum of two palindromes?
What are the numbers that can be expressed as the sum of two palindromes?
A number is a palindrome if it is the same written backwards, like 1367631.
My motivation comes from the problem posed for ...
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Probability of sequence of coin flips palindrome
I am flipping a coin at least 3 times, and then until the sequence of coin flips is a palindrome. What is the mean number of flips I will perform? What is the probability I won't stop?
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Is it true that there are infinite palindromic primes that when squared give palindromic number? [closed]
Can you prove that there are infinite palindromic primes that when squared give a palindromic number?
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Palindromes in the Möbius sequence
This question was already asked earlier at MSE.
Let $M$ denote the sequence of values of $\mu(n)$, the Möbius function which begins $M = (1,-1,-1,0,-1,1,-1,0,\dotsc)$. The questions below concern ...
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Conjecture on palindromic numbers
The conjecture is as follows:
Let $n\in\mathbb{N}\setminus\{1\}$. Define $a(n)=2^n+1$ and the set:
$$S(n) = \{ (a(n)^m+1)/2\ :\ m\in \mathbb{N}_0\}.$$
Then for all $c\in\mathbb{N}$, the number $(a(n)...
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simple conjecture on palindromes in base 10 [closed]
The conjecture says that for any a, b belong to the the set of non-negative integers ($a$ and $b$ are not necessarily distinct), taking any natural value of $c$; we have always that $$(10^c-1) \cdot \...
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Can a number be palindromic in more than 3 consecutive number bases?
$2017:$ Was initially asked on MSE - but wasn't solved or updated there since.
Update $2019$: I've returned to this problem, made some progress and updated the post here. (I've basically rewritten ...
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Is every integer greater than 1 the sum of a palindrome and a prime?
Helfgott proved that any odd number greater than 5 is the sum of three primes. Cilleruelo and Luca proved that every positive integer is the sum of three palindromes.
Is every integer greater than 1 ...
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Is there an arbitrarily long arithmetic progression whose members are palindromes?
I suspect there isn't for some simple reason, but I could not find anything on it and if the opposite would hold in a more general sense, then that would solve this question.
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Combinatorics of palindromic decompositions
This is sort of a companion to my question Number of trivializations of a trivial word in the free group (which in turn is motivated by my earlier question here). It turns out that that question may ...
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$\left[x,y\right]$ as a product of palindromes of even length?
I'm working on some palindromic words right now. Those are the elements of $F_2$, the free group on two generators, which are the same if reveresed. For example $xyx, y^2, xyxxyx$ and so on.
Can you ...
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Does there exist $a,n \in \mathbb{Z}^+$, where $n \geq 2$, such that $a, an, an^2,an^3,\ldots,an^5$ are all palindromes in base 10?
Question: Does there exist $a,n \in \mathbb{Z}^+$, where $n \geq 2$, such that $$a, an, an^2,an^3,\ldots,an^5$$ are all palindromes in base 10?
We see that $a=1$ and $n=11$ give rise to $$1, 11, 121, ...
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Palindromic continued fraction
Here's what I hope is a final question outside of my area that I need to understand a problem about stable vector bundles on $\mathbb{P}^2$. Thank you everybody for your help so far!
Suppose I have ...
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