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 #10 Mar 01 2020 12:08:12
%S 15,5,5,5,19,1,9,9,150,50,50,50,182,18,82,82,191,9,91,91,195,5,95,95,
%T 199,1,99,99,1500,500,500,500,1819,181,819,819,1950,50,950,950,1981,
%U 19,981,981,1991,9,991,991,1995,5,995,995,1999,1,999,999,15000,5000,5000,5000,18182,1818,8182,8182
%N Lexicographically earliest sequence of positive terms such that a(4n+1) is the sum of the next three terms, those three terms having the property that each of them is a substring of a(4n+1).
%C The sequence is infinite as one can always multiply a(4n+1) by 10 and do the same with the next three terms. It is conjectured that at least two of those three terms must be equal.
%H Éric Angelini, <a href="https://mailman.xmission.com/cgi-bin/mailman/private/math-fun/2020-February/034416.html">post to Math-Fun</a>
%e For n = 0, we have a(4n+1) = a(1) = 15 and 15 is the sum 5 + 5 + 5, those last three terms being a(2), a(3), a(4) and substrings of a(1);
%e For n = 3, we have a(4n+1) = a(13) = 182 and 182 is the sum 18 + 82 + 82, those last three terms being a(14), a(15), a(16) and substrings of a(13).
%K base,nonn
%O 1,1
%A _Eric Angelini_ and _Tom Duff_, Feb 26 2020