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 A335315 Lexicographically earliest sequence of distinct positive integers such that the sum of digits of any consecutive pair of terms divides their consecutive concatenation. 0
 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, 32, 31, 41, 48, 24, 45, 50, 44, 25, 34, 35, 28, 56, 52, 38, 42, 60, 62, 9, 54, 39, 27, 55, 65, 17, 29, 70, 33, 66, 47, 46, 80 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: This is a permutation of the natural numbers. The concatenation of any pair of adjacent terms is a composite number. LINKS EXAMPLE 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... MATHEMATICA 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 *) PROG (Python) def sumdigits(n):    return sum(int(i) for i in list(str(n))) def concat(a, b):    return int(str(a)+str(b)) def addterm(l):    n, i=l[-1], 1    while True:       c=concat(n, i)       if c % sumdigits(c)==0 and i not in l:          return l+[i]       i+=1 def seq(n):    sequence=    while len(sequence)

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Last modified July 29 23:58 EDT 2021. Contains 346346 sequences. (Running on oeis4.)