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A212278
Number of adjacent pairs of zeros (possibly overlapping) in the representation of n in base of Fibonacci numbers (A014417).
1
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
OFFSET
0,6
COMMENTS
a(n) = 0 only if n = Fibonacci(k)-1.
LINKS
EXAMPLE
A014417(5) = 1000, two pairs of adjacent zeros, so a(5) = 2.
MAPLE
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:
seq(a(n), n=0..150); # Alois P. Heinz, May 18 2012
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Alex Ratushnyak, May 13 2012
STATUS
approved