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A326806 Numbers k such that k multiplied by the sum of all its digits contains k as a substring.

%I A326806 #26 Oct 20 2019 07:33:53
%S A326806 0,1,5,6,10,19,28,37,46,50,55,60,64,73,82,91,100,109,118,127,136,145,
%T A326806 154,163,172,181,190,208,217,226,235,244,253,262,271,280,307,316,325,
%U A326806 334,343,352,361,370,406,415,424,433,442,451,460,500,505,514,523,532
%N A326806 Numbers k such that k multiplied by the sum of all its digits contains k as a substring.
%C A326806 Inspired by A328095.
%C A326806 Contains all numbers whose digit sum is a power of 10.
%C A326806 Contains all numbers of the form 5*10^k and 6*10^k. Terms which are not in the sets above are: 0, 6667, 58824, 8823529412, ... - _Chai Wah Wu_, Oct 19 2019
%H A326806 Alois P. Heinz, <a href="/A326806/b326806.txt">Table of n, a(n) for n = 1..10000</a>
%p A326806 a:= proc(n) option remember; local k; if n=1 then 0 else
%p A326806       for k from 1+a(n-1) while searchtext(cat(k), cat(k*
%p A326806       add(i, i=convert(k, base, 10))))=0 do od: k fi
%p A326806     end:
%p A326806 seq(a(n), n=1..75);
%o A326806 (Python)
%o A326806 n, A326806_list = 0, []
%o A326806 while len(A326806_list) < 10000:
%o A326806     sn = str(n)
%o A326806     if sn in str(n*sum(int(d) for d in sn)):
%o A326806         A326806_list.append(n)
%o A326806     n += 1 # _Chai Wah Wu_, Oct 19 2019
%Y A326806 Cf. A007953, A011557, A326811, A328095.
%K A326806 nonn,base
%O A326806 1,3
%A A326806 _Alois P. Heinz_, Oct 19 2019