Smallest numbers

Smallest 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.

Task

Smallest number k > 0 such that the decimal expansion of k^k contains n, where n < 51

REXX

<lang rexx>/*REXX pgm finds the smallest positive integer K where k**k contains N, N < 51 */ numeric digits 200 /*ensure enough decimal digs for k**k */ parse arg hi cols . /*obtain optional argument from the CL.*/ if hi== | hi=="," then hi= 51 /*Not specified? Then use the default.*/ if cols== | cols=="," then cols= 10 /* " " " " " " */ w= 6 /*width of a number in any column. */ @spiKK= ' smallest positive integer K where k**k contains N, N < ' commas(hi) say ' N │'center(@spiKK, 5 + cols*(w+1) ) /*display the title of the output. */ say '─────┼'center("" , 5 + cols*(w+1), '─') /* " " separator " " " */ $=; idx= 0 /*define $ output list; index to 0.*/

    do j=0  for hi;            n= j + 1         /*look for a power of 6 that contains N*/
                   do k=1  until pos(j, k**k)>0 /*calculate a bunch of powers  (K**K). */
                   end   /*k*/
    c= commas(k)                                /*maybe add commas to the powe of six. */
    $= $ right(c, max(w, length(c) ) )          /*add a  K (power) ──► list, allow big#*/
    if n//cols\==0 | j==0  then iterate         /*have we populated a line of output?  */
    say center(idx, 5)'│'substr($, 2);     $=   /*display what we have so far  (cols). */
    idx= idx + cols                             /*bump the  index  count for the output*/
    end   /*j*/

if $\== then say center(idx, 5)"│"substr($, 2) /*possible display residual output.*/ say '─────┴'center("" , 5 + cols*(w+1), '─') /* " " separator " " " */ exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?</lang>

output   when using the default inputs:

  N  │    smallest positive integer   K   where  k**k  contains  N,   N  <  51
─────┼───────────────────────────────────────────────────────────────────────────
  0  │     9      1      3      5      2      4      4      3      7      9
 10  │    10     11      5     19     22     26      8     17     16     19
 20  │     9      8     13      7     17      4     17      3     11     18
 30  │    13      5     23     17     18      7     17     15      9     18
 40  │    16     17      9      7     12     28      6     23      9     24
 50  │    23

Ring

<lang ring> load "stdlib.ring"

decimals(0) see "working..." + nl see "Smallest number k > 0 such that the decimal expansion of k^k contains n are:" + nl

row = 0 limit1 = 49 limit2 = 30

for n = 0 to limit1

   strn = string(n)
   for m = 1 to limit2
       powm = pow(m,m)
       strm = string(powm)
       ind = substr(strm,strn)
       if ind > 0
          exit
       ok
   next
   row = row + 1
   see "" + m + " "
   if row%10 = 0
      see nl
   ok

next

see "done..." + nl </lang>

Output:

working...
Smallest number k > 0 such that the decimal expansion of k^k contains n are:
9 1 3 5 2 4 4 3 7 9 
10 11 5 19 21 18 8 25 16 19 
9 8 13 7 17 4 17 3 11 18 
13 5 19 17 18 7 17 15 9 15 
16 18 9 7 12 25 6 23 9 23 
done...