

A067581


a(n) = smallest integer not yet in the sequence with no digits in common with a(n1), a(0)=0.


26



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
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OFFSET

0,3


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


LINKS



EXAMPLE

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.


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 *)


PROG

(Haskell)
import Data.List (delete, intersect); import Data.Function (on)
a067581 n = a067581_list !! (n1)
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
(PARI) {u=0; a=0; for(n=0, 99, print1(a", "); u+=1<<a; D=Set(if(a, digits(a))); for(k=0, 9e9, bittest(u, k)&&next; #setintersect(D, Set(digits(k)))&&next; a=k; break))} \\ 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


CROSSREFS



KEYWORD



AUTHOR

Ulrich Schimke (ulrschimke(AT)aol.com)


EXTENSIONS



STATUS

approved



