A067581 a(n) = smallest integer not yet in the sequence with no digits in common with a(n-1), a(0)=0.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 22, 11, 20, 13, 24, 15, 23, 14, 25, 16, 27, 18, 26, 17, 28, 19, 30, 12, 33, 21, 34, 29, 31, 40, 32, 41, 35, 42, 36, 44, 37, 45, 38, 46, 39, 47, 50, 43, 51, 48, 52, 49, 53, 60, 54, 61, 55, 62, 57, 63, 58, 64, 59, 66, 70, 56, 71, 65, 72, 68, 73, 69

Offset: 0

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Keywords

• easy
• nonn
• base
• nice
• look

Comments

David W. Wilson has shown that the sequence contains every positive integer except those containing all the digits 1 through 9 (which obviously have no possible predecessor). Jun 04 2002

a(A137857(n)) = A137857(n). - Reinhard Zumkeller, Feb 15 2008

Examples

			a(14) = 13, since a(13) = 20 and all integers smaller than 13 have a digit in common with 20 or have already appeared in the sequence.
		

Links

• Reinhard Zumkeller and Zak Seidov, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A136332, A184992, A239664, A249585, A249591.

See also A276512, A276633, A276766.

Programs

Haskell

import Data.List (delete, intersect); import Data.Function (on)
a067581 n = a067581_list !! (n-1)
a067581_list = 1 : f 1 [2..] where
   f u vs = v : f v (delete v vs)
     where v : _ = filter (null . (intersect `on` show) u) vs
-- Reinhard Zumkeller, Jul 01 2013

Mathematica

f[s_List] := Block[{k = 1, id = IntegerDigits@ s[[ -1]]}, While[ MemberQ[s, k] || Intersection[id, IntegerDigits@k] != {}, k++ ]; Append[s, k]]; Nest[f, {1}, 71] (* Robert G. Wilson v, Apr 03 2009 *)

PARI

{u=0; a=0; for(n=0, 99, print1(a", "); u+=1<M. F. Hasler, Nov 01 2014

Python

from itertools import count, islice, product as P
def only(s, D=1): # numbers with >= D digits only from s
    yield from (int("".join(p)) for d in count(D) for p in P(s, repeat=d))
def agen(): # generator of terms
    aset, an, minan = {0}, 0, 1
    while True:
        yield an
        an, s = minan, set(str(an))
        use = "".join(c for c in "0123456789" if c not in s)
        for an in only(use, D=len(str(minan))):
            if an not in aset: break
        aset.add(an)
        while minan in aset: minan += 1
print(list(islice(agen(), 73))) # Michael S. Branicky, Jun 30 2022

Extensions

Extended to a(0)=0 by M. F. Hasler, Nov 02 2014