A212278 Number of adjacent pairs of zeros (possibly overlapping) in the representation of n in base of Fibonacci numbers (A014417).

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

Author

Alex Ratushnyak, May 13 2012

Keywords

• base
• nonn

Comments

a(n) = 0 only if n = Fibonacci(k)-1.

Examples

			A014417(5) = 1000, two pairs of adjacent zeros, so a(5) = 2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10946

Crossrefs

Cf. A000045, A003714, A014417, A007895, A102364.

Programs

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