Lucky and even lucky numbers
Lucky numbers are positive integers that are formed by:
- take a list of all the positive integers
- remove every 2nd number
- take the 2nd number (which is 3 )
- remove every 3rd number
- take the 3rd number (which is 7 )
- remove every 7th number
- take the 4th number (which is 9 )
- remove every 9th number
- take the 5th number (which is 13 )
- remove every 13th number
- take the 6th number ···
Even lucky numbers are positive even integers that are formed by:
- take a list of all the positive even integers
- remove every 2nd number
- take the 2nd number (which is 4 )
- remove every 4th number
- take the 3rd number (which is 6 )
- remove every 6th number
- take the 4th number (which is 10 )
- remove every 10th number
- take the 5th number (which is 12 )
- remove every 12th number
- take the 6th number ···
The task's requirements are:
- write one or two subroutines (functions) to generate lucky numbers and even lucky numbers
- which kind of numbers and which number(s) will be specified via the command line or a similar interface.
- since input is from the command line, tests should be made for the common errors
- missing arguments
- too many arguments
- number (or numbers) aren't legal
- misspelled argument (lucky or evenLucky
- mixed case should be supported
- support for a particular number
- support for a range of particular numbers
- support for a range of values
The program should support the arguments:
what is displayed (on a single line)
argument(s) (optional verbage is encouraged)
╔═══════════════════╦═══════════════════════════════════════════════════╗
║ j ║ Jth lucky number ║
║ j , lucky ║ Jth lucky number ║
║ j , evenLucky ║ Jth even lucky number ║
║ ║ ║
║ j k ║ Jth through Kth (inclusive) lucky number ║
║ j k lucky ║ Jth through Kth (inclusive) lucky number ║
║ j k evenLucky ║ Jth through Kth (inclusive) even lucky number ║
║ ║ ║
║ j -k ║ all lucky numbers in the range j ──► |k| ║
║ j -k lucky ║ all lucky numbers in the range j ──► |k| ║
║ j -k evenLucky ║ all even lucky numbers in the range j ──► |k| ║
╚═══════════════════╩═══════════════════════════════════════════════════╝
where |k| is the absolute value of k
Specifically:
- show the first twenty lucky numbers
- show the first twenty even lucky numbers
- show all lucky numbers between 6,000 and 6,100 (inclusive)
- show all even lucky numbers in the same range as above
- show the 10,000th lucky number (extra credit)
- show the 10,000th even lucky number (extra credit)
REXX
<lang REXX>/*REXX program displays lucky or evenLucky integers (#'s or a # range).*/ parse arg bot top func _ . /*get what we need from the C.L. */ if func== then func='lucky' /*Not defined? Use the default. */ s=left('s',bot\==top & top\==",") /*plural results (or not plural).*/ say func 'number's":" bot top '───►' $lucky(bot, top, func, _) exit /*stick a fork in it, we're done.*/ /*────────────────────────────────$LUCKY subroutine─────────────────────*/ $lucky: arg x,y,f,?; if y== | y==',' then y=x /*get some vars.*/
- =0; $=; ny=y<0 /*set variable: NOY: value range*/
if f== then f='LUCKY'; lucky=f=='LUCKY' /*assume LUCKY if omitted*/ if f\=='LUCKY' & f\=='EVENLUCKY' then return 'function not valid: ' f if arg()>3 & ?\= then return "too many arguments entered: " ? if x= then return "1st argument is missing." if x<1 then return "1st argument isn't a positive integer: " x if \datatype(x,'W') then return "1st argument isn't an integer: " x if \datatype(y,'W') then return "2nd argument isn't an integer: " y if x>ay then return "2nd arg is less than 1st arg." ay=abs(y); yL=ay; if y>0 then yL=y*10+y+y /*adjust the upper Y limit. */ if f== then f='LUCKY'; lucky=f=='LUCKY'
/* [↓] build for LUCKY|EVENLUCKY*/ do j=1 until j>=yL /*construct list of pos integers.*/ if j//2==(\lucky) then iterate /*EVENLUCKY? Use only even ints.*/
if lucky then if (j+1)//6==0 then iterate /*prune if mod 6≡zero.*/
else nop /*balance the IF logic. */
else if j //8==0 then iterate /*prune next if mod 8≡0.*/
#=#+1 /*bump the counter of #'s found. */
$=$ j /*append integer to the $ list.*/
end /*j*/
z=0
do p=3 until z==; z=word($,p) /*start to prune the integer list*/
if z># then leave /*if integer is too large, stop. */
do j=#%z*z by -z to z /*elide every Zth int.*/
$=delword($,j,1) /*delete a particular #.*/
#=#-1 /*decrease integer count*/
end /*j*/ /*delete from right end.*/
end /*p*/
@.=
do k=1; parse var $ q $; if q== then leave; @.k=q; end /*k*/
@.0=k-1
do j=1 for # /*restrict the found integers. */
if (\ny & (j<x | j>ay)) | (ny & (@.j<x | @.j>ay)) then @.j=
end /*j*/ /* [↑] a list of #s or a range. */
_=
do b=1 for @.0; _=_ @.b; end /*build a list. */
return space(_) /*remove superfluous list blanks.*/</lang> output when the input is: 1 20 lucky
lucky numbers: 1 20 ───► 1 3 7 9 13 15 21 25 31 33 37 43 49 51 63 67 69 73 75 79
output when the input is: 1 20 evenLucky
evenLucky numbers: 1 20 ───► 2 4 6 10 12 18 20 22 26 34 36 42 44 50 52 54 58 68 70 76
output when the input is: 6000 -6100 lucky
lucky numbers: 6000 -6100 ───► 6009 6019 6031 6049 6055 6061 6079 6093
output when the input is: 6000 -6100 evenLucky
evenLucky numbers: 6000 -6100 ───► 6018 6020 6022 6026 6036 6038 6050 6058 6074 6090 6092
output when the input is: 10000
lucky number: 10000 ───► 115591
output when the input is: 10000 , evenLucky
evenLucky number: 10000 ───► 111842