%I
%S 1,2,4,5,10,8,20,7,11,16,30,6,3,12,15,21,19,26,18,36,40,14,13,23,22,
%T 32,31,41,48,24,45,50,44,25,34,35,28,56,52,38,42,60,62,9,54,39,27,55,
%U 65,17,29,70,33,66,47,46,80
%N Lexicographically earliest sequence of distinct positive integers such that the sum of digits of any consecutive pair of terms divides their consecutive concatenation.
%C Conjecture: This is a permutation of the natural numbers. The concatenation of any pair of adjacent terms is a composite number.
%e a(1) = 1 because this is the lexicographically earliest positive number. Then a(2) = 2 because 312. Then a(3) = 4 since 3 does not divide 23 but 6 divides 24. And so on...
%t sod[n_] := Plus @@ IntegerDigits@ n; c[x_, y_] := FromDigits[Join @@ IntegerDigits@ {x, y}]; L = {1}; Do[ k=1; s = sod@ Last@ L; While[ MemberQ[L, k]  Mod[ c[ Last@ L, k], s + sod@ k] != 0, k++]; AppendTo[L, k], {60}]; L (* _Giovanni Resta_, May 31 2020 *)
%o (Python)
%o def sumdigits(n):
%o return sum(int(i) for i in list(str(n)))
%o def concat(a,b):
%o return int(str(a)+str(b))
%o def addterm(l):
%o n,i=l[1],1
%o while True:
%o c=concat(n,i)
%o if c % sumdigits(c)==0 and i not in l:
%o return l+[i]
%o i+=1
%o def seq(n):
%o sequence=[1]
%o while len(sequence)<n:
%o sequence=addterm(sequence)
%o return sequence # David Nacin, May 31 2020
%Y Cf. A005349.
%K nonn,base
%O 1,2
%A _David James Sycamore_, May 31 2020
