A363079 - OEIS

%I #30 Apr 14 2024 04:44:40

%S 10,13,18,27,99,69,17,36,12,21,22,16,45,15,54,63,39,999,19,72,30,25,

%T 189,81,198,31,1899,499999999999999999999

%N The sum of the digits present in a(n) and a(n+1) divides exactly a(n). This is the lexicographically earliest infinite sequence of distinct positive terms having this property.

%C If we want the sequence to be infinite, we cannot extend it with terms < 10. After a(28) = 499999999999999999999 the terms become exponentially huge and impossible to present here.

%H Eric Angelini, <a href="http://cinquantesignes.blogspot.com/2023/07/supersums-superproducts.html">SuperSums, SuperProducts</a>, personal blog.

%e digitsum a(1) + digitsum a(2) = 1 + 0 + 1 + 3 = 5 and 5 divides exactly a(1) = 10;

%e digitsum a(2) + digitsum a(3) = 1 + 3 + 1 + 8 = 13 and 13 divides exactly a(2) = 13;

%e digitsum a(3) + digitsum a(4) = 1 + 8 + 2 + 7 = 18 and 18 divides exactly a(3) = 18;

%e digitsum a(4) + digitsum a(5) = 2 + 7 + 9 + 9 = 27 and 27 divides exactly a(4) = 27;

%e digitsum a(5) + digitsum a(6) = 9 + 9 + 6 + 9 = 33 and 33 divides exactly a(5) = 99; etc.

%Y Cf. A364120, A364187, A364188.

%K base,nonn

%O 1,1

%A _Eric Angelini_, Jul 13 2023