login
Lexicographically earliest sequence of distinct terms such that the cumulative sum [a(1)+a(2)+a(3)+... a(n)] is a multiple of the cumulative sum of the digits used by [a(1)+a(2)+a(3)... +a(n)].
1

%I #5 Oct 10 2018 09:09:27

%S 1,2,3,4,5,6,7,8,9,63,18,90,27,105,12,24,36,48,162,45,312,21,42,84,

%T 234,72,261,81,308,10,20,30,40,50,60,70,80,322,198,486,108,414,117,

%U 156,195,594,126,504,135,531,144,192,288,690,153,621,601,114,133,152,171,190,209,228,247,266,285,399,821,180,810,378,912,132,264,396,1752,216,1095,150,225,375,2603,112,140,224,252,280,336

%N Lexicographically earliest sequence of distinct terms such that the cumulative sum [a(1)+a(2)+a(3)+... a(n)] is a multiple of the cumulative sum of the digits used by [a(1)+a(2)+a(3)... +a(n)].

%H Jean-Marc Falcoz, <a href="/A320081/b320081.txt">Table of n, a(n) for n = 1..5001</a>

%e The sum of the first 9 terms is 45; the 10th term is 63 as the sum 45 + 63 (=108) is a multiple of 45+6+3 (=54);

%e the sum of the first 10 terms is 108; the 11th term is 18 as the sum 108 + 18 (=126) is a multiple of 54+1+8 (=63);

%e the sum of the first 11 terms is 126; the 12th term is 90 as the sum 126 + 90 (=216) is a multiple of 63+9+0 (=72);

%e the sum of the first 12 terms is 216; the 13th term is 27 as the sum 216 + 27 (=243) is a multiple of 72+2+7 (=81);

%e etc.

%K nonn,base,look

%O 1,2

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Oct 05 2018