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A341094
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a(1) = 0. Thereafter, if a(n) has appeared before, most recently at a(m), then a(n+1) = n-m-1, the number of terms between a(m) and a(n). Otherwise a(n+1)=1.
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2
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0, 1, 1, 0, 2, 1, 2, 1, 1, 0, 5, 1, 2, 5, 2, 1, 3, 1, 1, 0, 9, 1, 2, 7, 1, 2, 2, 0, 7, 4, 1, 5, 17, 1, 2, 7, 6, 1, 3, 21, 1, 2, 6, 5, 11, 1, 4, 16, 1, 2, 7, 14, 1, 3, 14, 2, 5, 12, 1, 5, 2, 4, 14, 7, 12, 6, 22, 1, 8, 1, 1, 0, 43, 1, 2, 13, 1, 2, 2, 0, 7, 16, 33
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OFFSET
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1,5
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COMMENTS
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Sequence is similar to A181391 except that the "count back" following a repeated term is 1 less, and the term following a first occurrence is 1 rather than 0. The plots are similar to those of the Van Eck sequence.
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LINKS
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Michael De Vlieger, Annotated scatterplot of a(n) for n = 1..256, showing records in red, terms otherwise appearing for the first time in green, zeros in blue, and indicating the smallest missing number in gold.
Michael De Vlieger, Scatterplot of a(n) for n = 1..16384 showing records in red and zeros in blue, and indicating the smallest missing number in gold.
Michael De Vlieger, Log-log scatterplot of a(n) for n = 1..2^20 showing records in red and indicating the smallest missing number in gold (ignoring zeros).
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EXAMPLE
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We start with a(1)=0, which has not appeared before, so a(2)=1, Likewise 1 has not appeared before so a(3) is also 1, which is a repeat term, last seen at a(2). Since there are no terms between the last two 1s, we have a(4)=0. We now have 0,1,1,0 and so a(5)=2, the number of terms between repetitions of zero. The only way a 0 appears in the sequence is as a consequence of adjacent identical terms k,k.
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MAPLE
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M := 100; # Adapted from the Maple program in A181391.
a := Array(1 .. M);
last := Array(0 .. M, -1);
m := M-1;
a[1] := 0;
a[2] := 1;
last[0] := 2;
nxt := 1;
for n from 3 to M do
hist := last[nxt];
a[n-1] := nxt;
last[nxt] := n;
nxt := 1;
if hist > 0 then nxt := n-hist-1; fi;
od:
[seq(a[n], n = 1 .. m)]
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MATHEMATICA
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a = {0}; Do[(AppendTo[a, If[IntegerQ@ c[#], i - c[#] - 1, 1]]; Set[c[#], i]) &@ a[[-1]], {i, 2, 83}]; a (* Michael De Vlieger, Feb 16 2022 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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