Difference between revisions of "1993 OIM Problems/Problem 1"
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== Problem == | == Problem == | ||
| − | A natural number is a palindrome if when written in decimal notation, it | + | A natural number is a palindrome if, when written in decimal notation, it is the same when written from left to right and from right to left; for example: 8, 23432, 6446. |
| − | Let <math>x_1<x_2 < \cdots < x_i<x_{i+1}< \cdots</math> all | + | Let <math>x_1<x_2 < \cdots < x_i<x_{i+1}< \cdots</math> be all the palindromes. For each <math>i</math>, let <math>y_{i+1} = x_{i+1}-x_i</math>. |
| − | How many different prime numbers does the set <math>{y_1,y_2,y_3,\cdots }</math> | + | How many different prime numbers does the set <math>{y_1,y_2,y_3,\cdots }</math> contain? |
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
| + | ~ Edits by [https://artofproblemsolving.com/wiki/index.php/User:Eevee9406 eevee9406] | ||
== Solution == | == Solution == | ||
Revision as of 18:16, 22 March 2025
Problem
A natural number is a palindrome if, when written in decimal notation, it is the same when written from left to right and from right to left; for example: 8, 23432, 6446.
Let 
be all the palindromes. For each 
, let 
.
How many different prime numbers does the set 
contain?
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com ~ Edits by eevee9406
Solution
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