%I #18 Dec 20 2023 08:04:28

%S 1,10,4,15,3,6,12,9,11,14,2,20,8,26,5,32,21,13,18,16,7,22,25,30,24,28,

%T 31,40,33,23,50,41,95,44,38,17,27,19,34,37,66,42,35,48,39,60,36,45,51,

%U 29,78,47,138,55,64,105,52,57,43,70,58,46,49,75,63,54,72,65,96,81,84,79

%N The sum of the digits present in a(n) and a(n+1) divides the product [a(n)*a(n+1)]. This is the lexicographically earliest sequence of distinct positive terms with this property.

%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 + 1 + 0 = 2 and 2 divides 1 * 10 = 10 (result = 5);

%e digitsum a(2) + digitsum a(3) = 1 + 0 + 4 = 5 and 5 divides 10 * 4 = 40 (result = 8);

%e digitsum a(3) + digitsum a(4) = 4 + 1 + 5 = 10 and 10 divides 4 * 15 = 60 (result = 6);

%e digitsum a(4) + digitsum a(5) = 1 + 5 + 3 = 9 and 9 divides 15 * 3 = 45 (result = 5);

%e digitsum a(5) + digitsum a(6) = 3 + 6 = 9 and 9 divides 3 * 6 = 18 (result = 2); etc.

%t a[1]=1; a[n_]:=a[n]=(k=1;While[MemberQ[Array[a,n-1],k]||Mod[a[n-1]*k,Total[Join[IntegerDigits@a[n-1],IntegerDigits@k]]]!=0,k++];k)

%t Array[a,60] (* _Giorgos Kalogeropoulos_, Jul 14 2023 *)

%Y Cf. A007953, A364120, A364187, A364188.

%K base,nonn

%O 1,2

%A _Eric Angelini_, Jul 12 2023