

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
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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

Table of n, a(n) for n=1..57.


EXAMPLE

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...


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=[1]
while len(sequence)<n:
sequence=addterm(sequence)
return sequence # David Nacin, May 31 2020


CROSSREFS

Cf. A005349.
Sequence in context: A125728 A276608 A173660 * A307805 A189767 A173817
Adjacent sequences: A335312 A335313 A335314 * A335316 A335317 A335318


KEYWORD

nonn,base


AUTHOR

David James Sycamore, May 31 2020


STATUS

approved



