 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  ProSum Numbers (Posted on 2015-01-28) 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 No Rating Comments: ( Back to comment list | You must be logged in to post comments.) 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 Please log in:

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