A227789 Sum of indices of Fibonacci numbers in Zeckendorf representation of n, assuming that the units place is Fibonacci(1).

0, 1, 3, 4, 5, 5, 6, 8, 6, 7, 9, 10, 11, 7, 8, 10, 11, 12, 12, 13, 15, 8, 9, 11, 12, 13, 13, 14, 16, 14, 15, 17, 18, 19, 9, 10, 12, 13, 14, 14, 15, 17, 15, 16, 18, 19, 20, 16, 17, 19, 20, 21, 21, 22, 24, 10, 11, 13, 14, 15, 15, 16, 18, 16, 17, 19, 20, 21, 17, 18, 20

Offset

0,3

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(1). The variant with 1 = Fibonacci(2) is A227788.

Links

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

Eric W. Weisstein, Zeckendorf Representation

Example

a(33) = 19 because Zeckendorf representation of 33 is 21+8+3+1, 21=F(8), 8=F(6), 3=F(4), 1=F(1), thus a(33) = 8+6+4+1 = 19.

Crossrefs

Cf. A000045, A003714, A227788.

Sequence in context: A065305 A009070 A200066 * A116183 A338233 A177744

Adjacent sequences: A227786 A227787 A227788 * A227790 A227791 A227792

Keyword

nonn

Author

Alex Ratushnyak, Sep 23 2013

Status

approved