A335315 - OEIS

%I #17 Jul 07 2020 06:13:38

%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 3|12. 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