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    ≥  100   will be considered for this Rosetta Code task.



Example

187   is a   gapful   number because it is evenly divisible by the
number   17   which is formed by the first and last decimal digits
of    187. 



About   7.46%   of positive integers are   gapful.



Task

   Generate and show all sets of numbers (below) on one line (horizontally) with a title,   here on this page
   Show the first   30   gapful numbers
   Show the first   15   gapful numbers    ≥           1,000,000
   Show the first   10   gapful numbers    ≥    1,000,000,000


Related tasks

   Harshad or Niven series.
   palindromic gapful numbers.
   largest number divisible by its digits.


Also see

   The OEIS entry:   A108343 gapful numbers.
   numbersaplenty gapful numbers


 
{def gapfuls
 {lambda {:n :i :N}
  {if {>= :i :N}
   then
   else {if {= {% :n {W.first :n}{W.last :n}} 0}
   then :n {gapfuls {+ :n 1} {+ :i 1} :N}
   else    {gapfuls {+ :n 1}    :i    :N}}}}} 
-> gapfuls 
 
{gapfuls 100 0 30}
-> 100 105 108 110 120 121 130 132 135 140 143 150 154 160 165 170 176 180
 187 190 192 195 198 200 220 225 231 240 242 253 
 
{gapfuls 1000000 0 15}
-> 1000000 1000005 1000008 1000010 1000016 1000020 1000021
 1000030 1000032 1000034 1000035 1000040 1000050 1000060 1000065 
 
{gapfuls 1000000000 0 10}
-> 1000000000 1000000001 1000000005 1000000008 1000000010
 1000000016 1000000020 1000000027 1000000030 1000000032
 