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Numbers n such that in some base b <= log n the sum of the digits of n in base b equals b.
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%I #7 Sep 24 2013 00:41:40

%S 9,10,12,17,18,20,21,24,29,31,33,34,36,37,39,40,45,48,55,57,63,65,66,

%T 67,68,70,72,73,76,80,82,83,85,87,88,91,93,96,97,99,100,109,111,112,

%U 117,129,130,132,133,135,136,144,145,148,153,157,160,161,163,165,171,177

%N Numbers n such that in some base b <= log n the sum of the digits of n in base b equals b.

%C The sequence A018900 refers to b=2. Other sequences with b=3,4,5,... could be considered separately. We present the case that includes the several b, provided that b<=Log(n) (this condition avoids trivial situations). - It is not completely clear how the sequence grows.

%e In base 4, 67=(1003)_4 and the sum 1+0+0+3 equals 4.

%t Seq = Function[{m}, Module[{ls, sk}, ls = {}; Do[Do[ sk = Apply[Plus, IntegerDigits[k, b]]; If[sk == b && E^b <= k, AppendTo[ls, k]], {b, 2, Log[k]}], {k, 1, m}]; Union[Sort[ls]] ]]; Seq[1000]

%Y In a sense this generalizes the sequence A018900 (if b=2 is considered).

%K nonn,base

%O 1,1

%A _Carlos Alves_, Dec 31 2002