We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

A positive whole number that is the same when reading from right to left and left to right is called a palindromic number. If all of them were put into a sequence that is from small to big:1,2...11,22...,101,111...,10001,10101,.....

Then which term is the number 78987 in this sequence? For example : 1 is the 1st term,2 is the second....etc

yomyhomies Oct 22, 2017

#2**+1 **

Starting with 0, 78987 is the 889th palindrome

[BTW...889 is known as the palindrome's* rank* ]

Starting with 1, it is the 888th palindrome

This can be verified with the calculator here :

http://rhyscitlema.com/algorithms/generating-palindromic-numbers/

[ The calculator is about half-way down the page.....there are also other intems of interest related to palindromes on this page ]

A procedure is desribed for finding the nth palindrome, but I don't see one that tells us how to determine the rank of any particular palindrome [ although I did not look at the page with a fine tooth comb]

Maybe heureka knows of a proceedure to produce this???

CPhill Oct 22, 2017

#3**+3 **

**which term is the number 78987 in this sequence?**

Here 0 is the 1st term:

The position of a **palindrome **within the sequence can be determined almost without calculation:

If the **palindrome **has an **even number of digits**,

prepend a 1 to the front half of the** palindrome's** digits.

Examples: 98766789=a(19876)

If the **number of digits is odd**, prepend the value of front digit + 1 to the digits from position 2 ... central digit.

Examples: 515=a(61), 8206028=a(9206), 9230329=a(10230).

see link: http://oeis.org/search?q=Palindromes+in+base+10

which term is the number **78987** in this sequence?

The **number of digits ****is 5**** is odd**, prepend the value of front digit + 1 to the digits from position 2 ... central digit.

\(\begin{array}{|rrrrll|} \hline & & & \Rsh & & \text{ until central digit} \\ &7 & 8 & 9 & 8 & 7 \\ &| & | & | \\ &+1 & | & | \\ &\downarrow & \downarrow & \downarrow \\ \text{term is } & \color{red}8 &\color{red}8 &\color{red} 9 \\ \hline \end{array} \)

Starting with 1, it is the **888th** palindrome

heureka
Oct 23, 2017