RosettaCodeData/Task/Palindromic-gapful-numbers/00-TASK.txt

Numbers   (positive integers expressed in base ten)   that are (evenly) divisible by the number formed by the
first and last digit are known as   '''gapful numbers'''.


''Evenly divisible''   means divisible with   no   remainder.


All   one─   and two─digit   numbers have this property and are trivially excluded.   Only
numbers &nbsp; <big> &ge; </big> '''100''' &nbsp; will be considered for this Rosetta Code task.


;Example:
<big>'''1037'''</big> &nbsp; is a &nbsp; '''gapful''' &nbsp; number because it is evenly divisible by the
number &nbsp; <big>'''17'''</big> &nbsp; which is formed by the first and last decimal digits
of &nbsp; <big> '''<u>1</u>03<u>7</u>'''. </big>


A palindromic number is &nbsp; (for this task, a positive integer expressed in base ten), &nbsp; when the number is 
reversed, &nbsp; is the same as the original number.


;Task:
:* &nbsp; Show &nbsp; (nine sets) &nbsp; the first &nbsp; '''20''' &nbsp; palindromic gapful numbers that &nbsp; ''end'' &nbsp; with:
:::* &nbsp; the digit &nbsp; '''1'''
:::* &nbsp; the digit &nbsp; '''2'''
:::* &nbsp; the digit &nbsp; '''3'''
:::* &nbsp; the digit &nbsp; '''4'''
:::* &nbsp; the digit &nbsp; '''5'''
:::* &nbsp; the digit &nbsp; '''6'''
:::* &nbsp; the digit &nbsp; '''7'''
:::* &nbsp; the digit &nbsp; '''8'''
:::* &nbsp; the digit &nbsp; '''9'''
:* &nbsp; Show &nbsp; (nine sets, like above) &nbsp; of palindromic gapful numbers:
:::* &nbsp; the last &nbsp; '''15''' &nbsp; palindromic gapful numbers &nbsp; (out of &nbsp; &nbsp; &nbsp;'''100''')
:::* &nbsp; the last &nbsp; '''10''' &nbsp; palindromic gapful numbers &nbsp; (out of &nbsp;              '''1,000''') &nbsp; &nbsp; &nbsp; {optional}


For other ways of expressing the (above) requirements, see the &nbsp; ''discussion'' &nbsp; page.


;Note:
All palindromic gapful numbers are divisible by eleven. 


;Related tasks:
:* &nbsp; [https://rosettacode.org/wiki/Palindrome_detection palindrome detection].
:* &nbsp; [https://rosettacode.org/wiki/Gapful_numbers gapful numbers].


;Also see:
:* &nbsp; The OEIS entry: &nbsp; [https://oeis.org/A108343 A108343 gapful numbers].
<br><br>