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A276766
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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.
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4
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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, 34, 19, 28, 31, 40, 21, 35, 41, 32, 45, 36, 42, 37, 46, 38, 47, 39, 48, 50, 43, 51, 49, 52, 60, 53, 61, 54, 62, 57, 63, 58, 64, 59, 67, 80, 56, 70, 65, 71, 68, 72, 69, 73, 81, 74, 82, 75
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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The author of this sequence is Rodolfo Kurchan, who mentioned this sequence in a Facebook Group "Series", cf. link.
The sequence is finite, with last term a(5274) = 78642. - M. F. Hasler, Sep 17 2016
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LINKS
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PROG
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(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
(Python)
def ok(s, t): return len(set(t)) == len(t) and len(set(s+t)) == len(s+t)
def agen(): # generator of complete sequence of terms
aset, k, mink, MAX = {0}, 0, 1, 987654321
while True:
if k < MAX: yield k
else: return
k, s = mink, str(k)
MAX = 10**(10-len(s))
while k < MAX and (k in aset or not ok(s, str(k))):
k += 1
aset.add(k)
while mink in aset: mink += 1
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CROSSREFS
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KEYWORD
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nonn,base,fini,full
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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