A332843 - 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