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%I #7 Nov 21 2013 12:50:05
%S 10,10,4,10,10,4,10,10,2,10,10,10,10,10,4,10,10,2,10,10,10,10,10,10,
%T 10,10,2,10,10,4,10,10,4,10,10,2,10,10,4,10,10,10,10,10,2,10,10,4,10,
%U 10,4,10,10,2,10,10,4,10,10,4,10,10,2,10,10,4,10,10,4,10,10,2,10,10,7,10,10
%N a(n) = smallest k > 1 such that n and kn have the same digit sum
%C 2 <= a(n) <= 10
%C Every number from 2 through 10 is in the sequence. a(9) = 2, a(144) = 3, a(3) = 4, a(243) = 5, a(5553) = 6, a(75) = 7, a(1314) = 8, a(6876) = 9, a(1) = 10. n !== 0 (mod 3) ==> a(n) = 10
%H D. W. Wilson, <a href="/A180011/b180011.txt">Table of n, a(n) for n=1..10000</a>
%p Digit sum of 15 = 6. The next multiple of 15 with digit sum 6 = 4*15 = 60, so a(15) = 4.
%t ds[n_]:=Module[{dsn=Total[IntegerDigits[n]],k=2},While[dsn!=Total[ IntegerDigits[k n]],k++];k]; Array[ds,80] (* _Harvey P. Dale_, Jan 16 2012 *)
%K base,easy,nonn
%O 1,1
%A _David W. Wilson_, Aug 06 2010
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