A227788 Sum of indices of Fibonacci numbers in Zeckendorf representation of n, assuming the units place is Fibonacci(2).

0, 2, 3, 4, 6, 5, 7, 8, 6, 8, 9, 10, 12, 7, 9, 10, 11, 13, 12, 14, 15, 8, 10, 11, 12, 14, 13, 15, 16, 14, 16, 17, 18, 20, 9, 11, 12, 13, 15, 14, 16, 17, 15, 17, 18, 19, 21, 16, 18, 19, 20, 22, 21, 23, 24, 10, 12, 13, 14, 16, 15, 17, 18, 16, 18, 19, 20, 22, 17, 19, 20

Offset

0,2

Comments

If n = F(i1) + F(i2) +...+ F(ik) is the Zeckendorf representation of n (i.e., write n in Fibonacci number system) then a(n) = i1 + i2 +...+ ik. 1 is Fibonacci(2). The variant with 1 = Fibonacci(1) is A227789.

Links

Table of n, a(n) for n=0..70.

Eric W. Weisstein, Zeckendorf Representation

Example

a(33) = 20 because Zeckendorf representation of 33 is 21 + 8 + 3 + 1 = F(8) + F(6) + F(4) + F(2), thus a(33) = 8 + 6 + 4 + 2 = 20.

Prog

(Python)
A003714 = [n for n in range(1, 300) if 2*n & n == 0]
print(0, end=', ')
for a in A003714:
  sum = 0
  i = 2
  while a:
    if a&1:  sum += i
    a >>= 1
    i += 1
  print(sum, end=', ')

Crossrefs

Cf. A000045, A003714, A227789.

Sequence in context: A361478 A332781 A066115 * A222245 A275582 A129607

Adjacent sequences: A227785 A227786 A227787 * A227789 A227790 A227791

Keyword

nonn,easy

Author

Alex Ratushnyak, Sep 23 2013

Status

approved