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A212278
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Number of adjacent pairs of zeros (possibly overlapping) in the representation of n in base of Fibonacci numbers (A014417).
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1
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0, 0, 0, 1, 0, 2, 1, 0, 3, 2, 1, 1, 0, 4, 3, 2, 2, 1, 2, 1, 0, 5, 4, 3, 3, 2, 3, 2, 1, 3, 2, 1, 1, 0, 6, 5, 4, 4, 3, 4, 3, 2, 4, 3, 2, 2, 1, 4, 3, 2, 2, 1, 2, 1, 0, 7, 6, 5, 5, 4, 5, 4, 3, 5, 4, 3, 3, 2, 5, 4, 3, 3, 2, 3, 2, 1, 5, 4, 3, 3, 2, 3, 2, 1, 3, 2, 1, 1, 0, 8
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OFFSET
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0,6
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COMMENTS
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a(n) = 0 only if n = Fibonacci(k)-1.
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LINKS
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EXAMPLE
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A014417(5) = 1000, two pairs of adjacent zeros, so a(5) = 2.
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MAPLE
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F:= combinat[fibonacci]:
b:= proc(n) option remember; local j;
if n=0 then 0
else for j from 2 while F(j+1)<=n do od;
b(n-F(j))+2^(j-2)
fi
end:
a:= proc(n) local c, h, m, t;
c, t, m:= 0, 1, b(n);
while m>0 do
h:= irem(m, 2, 'm');
if h=t and h=0 then c:=c+1 fi;
t:=h
od; c
end:
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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