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Equal digit sum (Posted on 2012-11-22) Difficulty: 5 of 5
Find all integers n such that S(n) = S(2n) = ... = S(n*n), where S is the sum of the base-10 digits.

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts computer exploration--no proof | Comment 2 of 4 |

DECLARE FUNCTION sod! (x!)
FOR n = 1 TO 9999999
    s = sod(n)
    good = 1
    FOR coef = 2 TO n
        IF sod(coef * n) <> s THEN good = 0: EXIT FOR
    NEXT coef
    IF good THEN PRINT n
NEXT n

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

finds only

1
9
99
999

Nothing else up to 10 billion.


  Posted by Charlie on 2012-11-22 12:08:45
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