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ProSum Numbers (Posted on 2015-01-28) Difficulty: 2 of 5
ProSum Numbers are obtained when the product of an integer's digits divided by the sum of its digits is itself an integer. If the resultant integer can be used to produce yet another integer in the same way, a sequence is formed. It is terminated when a new term is less than 10. The first term must be at least 10, or an endless loop is formed.

Find the lowest starting term for a sequence of two ProSum Numbers, then do the same for three terms and four terms.

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution computer solution | Comment 1 of 5
DECLARE FUNCTION sod# (x#)
DEFDBL A-Z
DIM r(10), found(10, 10)
CLS

FOR i = 10 TO 9999999
   n = i
   ct = 0
   DO
   ct2 = 0
   flag$ = ""
   s = sod(n)
   IF n MOD s = 0 THEN
     ct = ct + 1
     r(ct) = n
     IF n < 11 THEN EXIT DO
     n = n / s
     IF s = 1 THEN EXIT DO
   ELSE
     EXIT DO
   END IF
   LOOP
   IF found(ct, 0) = 0 THEN
      found(ct, 0) = i
      PRINT i, ct
      FOR j = 1 TO ct
         found(ct, j) = r(j)
         PRINT "     "; r(j)
      NEXT
      PRINT flag$
   END IF


NEXT i

'
FUNCTION sod (x)
   ns$ = LTRIM$(STR$(x))
   tot = 0
   FOR i = 1 TO LEN(ns$)
       tot = tot + VAL(MID$(ns$, i, 1))
   NEXT
   sod = tot
END FUNCTION

finds



 10            1
      10
 11            0
 12            2
      12
      4
 108           3
      108
      12
      4
 1080          4
      1080
      120
      40
      10
 19440         5
      19440
      1080
      120
      40
      10
      
So the lowest with two is 12,4; the lowest with three is 108,12,4 and the lowest with four is 1080,120,40,10. In addition, the lowest with five is  19440,1080,120,40,10. All these repeat thereafter, including the 2-digit 10.
     


  Posted by Charlie on 2015-01-28 11:19:45
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