Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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