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A276766 a(n) = smallest nonnegative integer not yet in the sequence with no repeated digits and no digits in common with a(n-1), starting with a(0)=0.

%I A276766 #31 May 31 2024 22:04:23
%S A276766 0,1,2,3,4,5,6,7,8,9,10,23,14,20,13,24,15,26,17,25,16,27,18,29,30,12,
%T A276766 34,19,28,31,40,21,35,41,32,45,36,42,37,46,38,47,39,48,50,43,51,49,52,
%U A276766 60,53,61,54,62,57,63,58,64,59,67,80,56,70,65,71,68,72,69,73,81,74,82,75
%N A276766 a(n) = smallest nonnegative integer not yet in the sequence with no repeated digits and no digits in common with a(n-1), starting with a(0)=0.
%C A276766 The author of this sequence is _Rodolfo Kurchan_, who mentioned this sequence in a Facebook Group "Series", cf. link.
%C A276766 The sequence is finite, with last term a(5274) = 78642. - _M. F. Hasler_, Sep 17 2016
%H A276766 M. F. Hasler, <a href="/A276766/b276766.txt">Table of n, a(n) for n = 0..5274</a> (All terms)
%H A276766 Rodolfo Kurchan, <a href="https://www.facebook.com/groups/1157552824271105/">Post in Facebook Group "Series"</a>.
%o A276766 (PARI) {u=[]; (t(k)=if(#Set(k=digits(k))==#k,k)); a=1; for(n=1, 99, print1(a","); u=setunion(u, [a]); t(u[1])||u[1]++; while(#u>1&&u[2]<=u[1]+1, u=u[^1]); for(k=u[1]+1, 9e9, setsearch(u, k)&&next; (d=t(k))&& !#setintersect(Set(digits(a)), Set(d))&&(a=k)&&next(2))); a} \\ _M. F. Hasler_, Sep 17 2016
%o A276766 (Python)
%o A276766 def ok(s, t): return len(set(t)) == len(t) and len(set(s+t)) == len(s+t)
%o A276766 def agen(): # generator of complete sequence of terms
%o A276766     aset, k, mink, MAX = {0}, 0, 1, 987654321
%o A276766     while True:
%o A276766         if k < MAX: yield k
%o A276766         else: return
%o A276766         k, s = mink, str(k)
%o A276766         MAX = 10**(10-len(s))
%o A276766         while k < MAX and (k in aset or not ok(s, str(k))):
%o A276766             k += 1
%o A276766         aset.add(k)
%o A276766         while mink in aset: mink += 1
%o A276766 print(list(agen())[:73]) # _Michael S. Branicky_, Jun 30 2022
%Y A276766 Cf. A054659, A067581, A276633, A276512.
%K A276766 nonn,base,fini,full
%O A276766 0,3
%A A276766 _Claudio Meller_, Sep 17 2016
%E A276766 Edited by _M. F. Hasler_, Sep 17 2016