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%I #13 Feb 01 2022 01:36:35
%S 0,1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100,109,200,300,400,
%T 500,600,700,800,910,1000,1009,1090,2000,3000,4000,5000,6000,7000,
%U 8000,9000,9010,9100,10000,10009,10090,10900,20000,30000,40000,50000,60000,70000
%N Numbers n with k digits such that each sum of 1, 2, ..., k digits of n is a substring of n.
%C Conjecture: sequence contains only
%C - numbers of the form k*10^j (j>=0, k>=0),
%C - numbers of the form 10X, where X = string of k digits containing one digit 9 and k-1 digits 0 (k>=1),
%C - numbers of form 9Y10Z; where Y = string of k digits 0 (k>=0), Z = string of j digits 0 (j>=0).
%C Subsequence of A052018.
%e 109 is a term because all possible sums of digits 0, 1, 1, 9, 9, 10 are its substrings.
%Y Cf. A052018 (numbers k such that the sum of the digits of k is substring of k).
%K nonn,base
%O 1,3
%A _Jaroslav Krizek_, Jan 06 2012
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