%I #37 Jul 01 2022 05:33:50

%S 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,

%T 19,30,12,33,21,34,29,31,40,32,41,35,42,36,44,37,45,38,46,39,47,50,43,

%U 51,48,52,49,53,60,54,61,55,62,57,63,58,64,59,66,70,56,71,65,72,68,73,69

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

%C 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

%C a(A137857(n)) = A137857(n). - _Reinhard Zumkeller_, Feb 15 2008

%H Reinhard Zumkeller and Zak Seidov, <a href="/A067581/b067581.txt">Table of n, a(n) for n = 0..10000</a>

%e 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.

%t 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 *)

%o (Haskell)

%o import Data.List (delete, intersect); import Data.Function (on)

%o a067581 n = a067581_list !! (n-1)

%o a067581_list = 1 : f 1 [2..] where

%o f u vs = v : f v (delete v vs)

%o where v : _ = filter (null . (intersect `on` show) u) vs

%o -- _Reinhard Zumkeller_, Jul 01 2013

%o (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

%o (Python)

%o from itertools import count, islice, product as P

%o def only(s, D=1): # numbers with >= D digits only from s

%o yield from (int("".join(p)) for d in count(D) for p in P(s, repeat=d))

%o def agen(): # generator of terms

%o aset, an, minan = {0}, 0, 1

%o while True:

%o yield an

%o an, s = minan, set(str(an))

%o use = "".join(c for c in "0123456789" if c not in s)

%o for an in only(use, D=len(str(minan))):

%o if an not in aset: break

%o aset.add(an)

%o while minan in aset: minan += 1

%o print(list(islice(agen(), 73))) # _Michael S. Branicky_, Jun 30 2022

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

%Y See also A276512, A276633, A276766.

%K easy,nonn,base,nice,look

%O 0,3

%A Ulrich Schimke (ulrschimke(AT)aol.com)

%E Extended to a(0)=0 by _M. F. Hasler_, Nov 02 2014