login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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 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=[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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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