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A344486 a(n) is the least k such that the sum of digits of k is a substring of n and the sum of digits of n is a substring of k.

%I A344486 #6 May 27 2021 06:32:17
%S A344486 0,1,2,3,4,5,6,7,8,9,1,29,39,49,59,69,79,89,99,10,2,399,499,599,699,
%T A344486 799,899,999,101,11,3,4999,5999,6999,7999,8999,9999,102,111,12,4,
%U A344486 59999,69999,79999,89999,99999,103,112,112,13,5,699999,799999,899999,999999
%N A344486 a(n) is the least k such that the sum of digits of k is a substring of n and the sum of digits of n is a substring of k.
%C A344486 The sequence is well defined:
%C A344486 - for any number n with sum of digits d,
%C A344486 - by necessity, d <= n,
%C A344486 - the number k obtained by concatenating n-d 1's in front of d meets the requirements.
%H A344486 Rémy Sigrist, <a href="/A344486/a344486.pl.txt">Perl program for A344486</a>
%F A344486 a(10 * n) = a(n).
%e A344486 For n = 11:
%e A344486 - the sum of digits of 11 is 2,
%e A344486 - the sum of digits of a(n) must equal 1 or 11,
%e A344486     - the numbers whose sum of digits is 1 are the powers of 10,
%e A344486     - 2 cannot be a substring of a power of 10,
%e A344486     - the first number with sum of digits 11 is 29,
%e A344486     - 2 is a substring of 29,
%e A344486 - so a(11) = 29.
%o A344486 (Perl) See Links section.
%Y A344486 Cf. A007953, A052018, A344487.
%K A344486 nonn,base
%O A344486 0,3
%A A344486 _Rémy Sigrist_, May 21 2021