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
Reinhard Zumkeller and Zak Seidov, Table of n, a(n) for n = 0..10000
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 !! (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
(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
print(list(islice(agen(), 73))) # Michael S. Branicky, Jun 30 2022
CROSSREFS
KEYWORD
AUTHOR
Ulrich Schimke (ulrschimke(AT)aol.com)
EXTENSIONS
Extended to a(0)=0 by M. F. Hasler, Nov 02 2014
STATUS
approved