Gapful numbers

Gapful numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Numbers   (expressed in base ten)   that are (evenly) divisible by the number formed by the decimal digits of their first and last digit are known as   gapful numbers.

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.

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

Also see

•   The OEIS entry:   A108343 gapful numbers.

Factor

<lang factor>USING: formatting kernel lists lists.lazy math math.functions math.text.utils sequences ;

gapful? ( n -- ? )

   dup 1 digit-groups [ first ] [ last 10 * + ] bi divisor? ;

30 100 15 1,000,000 10 1,000,000,000 [

   2dup lfrom [ gapful? ] lfilter ltake list>array
   "%d gapful numbers starting at %d:\n%[%d, %]\n\n" printf

] 2tri@</lang>

Output:

30 gapful numbers starting at 100:
{ 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 }

15 gapful numbers starting at 1000000:
{ 1000000, 1000005, 1000008, 1000010, 1000016, 1000020, 1000021, 1000030, 1000032, 1000034, 1000035, 1000040, 1000050, 1000060, 1000065 }

10 gapful numbers starting at 1000000000:
{ 1000000000, 1000000001, 1000000005, 1000000008, 1000000010, 1000000016, 1000000020, 1000000027, 1000000030, 1000000032 }

Perl 6

Works with: Rakudo version 2019.07.1

Also test starting on a number that doesn't start with 1. Required to have titles, may as well make 'em noble. :-)

<lang perl6>use Lingua::EN::Numbers;

for (1e2, 30, 1e6, 15, 1e9, 10, 7123, 25)».Int -> $start, $count {

   put "\nFirst $count gapful numbers starting at {comma $start}:\n" ~
   <Sir Lord Duke King>.pick ~ ": ", ~
   ($start..*).grep( { $_ %% .comb[0, *-1].join } )[^$count];

}</lang>

Output:

First 30 gapful numbers starting at 100:
Sir: 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

First 15 gapful numbers starting at 1,000,000:
Duke: 1000000 1000005 1000008 1000010 1000016 1000020 1000021 1000030 1000032 1000034 1000035 1000040 1000050 1000060 1000065

First 10 gapful numbers starting at 1,000,000,000:
King: 1000000000 1000000001 1000000005 1000000008 1000000010 1000000016 1000000020 1000000027 1000000030 1000000032

First 25 gapful numbers starting at 7,123:
King: 7125 7140 7171 7189 7210 7272 7275 7280 7296 7350 7373 7420 7425 7474 7488 7490 7560 7575 7630 7632 7676 7700 7725 7770 7777

Python

<lang python>from itertools import islice, count for start, n in [(100, 30), (1_000_000, 15), (1_000_000_000, 10)]:

   print(f"\nFirst {n} gapful numbers from {start:_}")
   print(list(islice(( x for x in count(start) 
                       if (x % (int(str(x)[0]) * 10 + (x % 10)) == 0) )
                     , n)))</lang>

Output:

First 30 gapful numbers from 100
[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]

First 15 gapful numbers from 1_000_000
[1000000, 1000005, 1000008, 1000010, 1000016, 1000020, 1000021, 1000030, 1000032, 1000034, 1000035, 1000040, 1000050, 1000060, 1000065]

First 10 gapful numbers from 1_000_000_000
[1000000000, 1000000001, 1000000005, 1000000008, 1000000010, 1000000016, 1000000020, 1000000027, 1000000030, 1000000032]

REXX

<lang rexx>/*REXX program computes and displays gapful numbers and also palindromic gapful numbers.*/ numeric digits 20 /*ensure enough decimal digits gapfuls.*/ parse arg gapfuls /*obtain optional arguments from the CL*/ if gapfuls= then gapfuls= 30 15@10000000 10@100000000000 /*assume defaults. */

       do until gapfuls=;      parse var gapfuls stuff gapfuls;       call gapful stuff
       end   /*until*/

exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ gapful: procedure; parse arg n '@' sp; #= 0; if sp== then sp= 100

       say center(' 'n      " gapful numbers starting at: "     sp' ', 140, "═")
       $=                                                          /*initialize $ list.*/
            do j=sp  until #==n                                    /*SP:  start point. */
            parse var   j   a  2    -1  b                        /*get 1st & last dig*/
            if j // (a||b) \== 0  then iterate                     /*perform ÷ into  J.*/
            #= # + 1;             $= $ j                           /*bump #; append──►$*/
            end   /*j*/
       say strip($);     say;     return</lang>

output   when using the default inputs:

(Shown at   ⁵/₆   size.)

═══════════════════════════════════════════════════ 30  gapful numbers starting at:  100 ═══════════════════════════════════════════════════
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

════════════════════════════════════════════════ 15  gapful numbers starting at:  10000000 ═════════════════════════════════════════════════
10000000 10000001 10000003 10000004 10000005 10000008 10000010 10000016 10000020 10000030 10000032 10000035 10000040 10000050 10000060

══════════════════════════════════════════════ 10  gapful numbers starting at:  100000000000 ═══════════════════════════════════════════════
100000000000 100000000001 100000000005 100000000008 100000000010 100000000016 100000000020 100000000030 100000000032 100000000035