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palindromic number (Definition)

An integer $ n$ that in a given base $ b$ is a palindrome. Given $ n$ being $ k$ digits $ d_x$ long in base $ b$, its value being

$\displaystyle n = \sum_{i = 0}^{k - 1} d_kb^i$
then if the equalities $ d_k = d_1$, $ d_{k - 1} = d_2$, etc., hold, then $ n$ is a palindromic number. There are infinitely many palindromic numbers in any given base.



"palindromic number" is owned by CompositeFan. [ owner history (1) ]
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palindromic prime (Definition) by PrimeFan
sequences $b^{2n}-1$ and $b^{2n-1}+1$ are divisible by $b+1$ (Derivation) by perucho
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Cross-references: equalities, digits, palindrome, base, integer
There are 11 references to this entry.

This is version 1 of palindromic number, born on 2006-05-27.
Object id is 7931, canonical name is PalindromicNumber.
Accessed 1148 times total.

Classification:
AMS MSC: 11A63 (Number theory :: Elementary number theory :: Radix representation; digital problems)
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a note about 11| { } by perucho on 2006-09-08 15:32:05
Let k,n denote positive integer numbers. It is easy to see that the sequences a_k=10^{2k-1}+1 and b_n=10^{2n}-1 are divisible by 11. Hence 11|a_k+b_n. From this, it is easy to prove that 11 divides every even length palindromic number.
perucho
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