Talk:Rare numbers

comments concerning interesting observations from an webpage

(The author's webpage, the last URL reference from this task's preamble, re-shown below:)

(a URL reference):

author's website: rare numbers by Shyam Sunder Gupta. (lots of hints and some observations).

I was considering adding checks (to the REXX program) to assert that for:

when the number of digits in a rare number is even, the sum must be divisible by 11, and
when the number of digits in a rare number is odd, the difference must be divisible by 9.

In fact, all the other (previous) checks (in the REXX program) have already filtered out the two (above) wrong cases, so the above two interesting observations are never observed to be false, so the checks are (at that point) in fact, redundant.

In fact, the webpage section contains a errors, the difference must be divisible by 9, not 11 as it states in the text.

Also, the mention of A² and B² having to be divisible by some number seems to be also wrong. I'm attempting to contact the author via e-mail. -- Gerard Schildberger (talk) 20:59, 8 September 2019 (UTC)

the 1^st REXX version

This is the 1^st REXX version, before all the optimizations were added: <lang rexx>/*REXX program to calculate and display an specified amount of rare numbers. */ numeric digits 20; w= digits() + digits() % 3 /*ensure enough decimal digs for calcs.*/ parse arg many start . /*obtain optional argument from the CL.*/ if many== | many=="," then many= 3 /*Not specified? Then use the default.*/

= 0 /*the number of rare numbers (so far)*/

   do n=10                                      /*N=10, 'cause 1 dig #s are palindromic*/
   r= reverse(n)                                /*obtain the reverse of the number  N. */
   if r>n   then iterate                        /*Difference will be negative?  Skip it*/
   if n==r  then iterate                        /*Palindromic?   Then it can't be rare.*/
   s= n+r                                       /*obtain the    sum     of  N  and  R. */
   d= n-r                                       /*   "    "  difference  "  "   "   "  */
   if iSqrt(s)**2 \== s  then iterate           /*Not a perfect square?  Then skip it. */
   if iSqrt(d)**2 \== d  then iterate           /* "  "    "       "       "    "   "  */
   #= # + 1                                     /*bump the counter of  rare  numbers.  */
   say right( th(#), length(#) + 9)       ' rare number is:  '       right( commas(n), w)
   if #>=many  then leave                       /* [↑]  W:  the width of # with commas.*/
   end   /*n*/

exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg _; do jc=length(_)-3 to 1 by -3; _=insert(',', _, jc); end; return _ th: parse arg th;return th||word('th st nd rd',1+(th//10)*(th//100%10\==1)*(th//10<4)) /*──────────────────────────────────────────────────────────────────────────────────────*/ iSqrt: parse arg x; $= 0; q= 1; do while q<=x; q= q*4

                                                                 end  /*while q<=x*/
                 do while q>1;  q= q % 4;   _= x-$-q;   $= $ % 2
                 if _>=0  then do;          x= _;       $= $ + q
                               end
                 end   /*while q>1*/;                            return $</lang>

Pretty simple, but slow as molasses in January.

Not ready for prime time.

comments concerning interesting observations from an webpage

the 1st REXX version

the 1^st REXX version