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A248040 Numbers n such that n*digsum(n) contains the same distinct digits as n.

%I A248040 #24 May 06 2022 13:13:51
%S A248040 1,10,100,109,190,208,280,307,370,406,450,460,505,550,604,640,703,730,
%T A248040 802,820,901,910,1000,1009,1018,1027,1036,1045,1054,1063,1072,1081,
%U A248040 1090,1108,1168,1180,1207,1270,1286,1306,1360,1405,1450,1504,1540,1603,1630,1702,1720,1726,1801
%N A248040 Numbers n such that n*digsum(n) contains the same distinct digits as n.
%C A248040 10^k is a subsequence for k >= 0. Thus this sequence is infinite.
%H A248040 Robert Israel, <a href="/A248040/b248040.txt">Table of n, a(n) for n = 1..10000</a>
%p A248040 filter:= proc(n) local L,s,d;
%p A248040   L:= convert(n,base,10);
%p A248040   d:= convert(L,set);
%p A248040   s:= convert(L,`+`);
%p A248040   evalb(convert(convert(n*s,base,10),set)=d)
%p A248040 end proc:
%p A248040 select(filter, [$1..2000]); # _Robert Israel_, Mar 06 2018
%o A248040 (PARI) for(n=1,10^4,d=digits(n);if(vecsort(d,,8)==vecsort(digits(n*sumdigits(n)),,8),print1(n,", ")))
%Y A248040 Cf. A007953 (sum of digits), A011557 (powers of 10).
%Y A248040 Cf. A247888 (similar, with n + product of digits), A247887 (similar, with n + digsum).
%K A248040 nonn,base,easy
%O A248040 1,2
%A A248040 _Derek Orr_, Sep 30 2014