

A227788


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


1



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
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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 = [
# insert nonzero terms of A003714 here
1, 2, 4, 5, 8, 9, 10, 16, 17, 18, 20, 21, 32, 33, 34, 36, 37, 40, 41, 42, 64, 65, 66, 68
]
print 0,
for a in A003714:
sum = 0
i = 2
while a:
if a&1: sum += i
a >>= 1
i += 1
print sum,


CROSSREFS

Cf. A000045, A003714, A227789.
Sequence in context: A266447 A100700 A066115 * A222245 A275582 A129607
Adjacent sequences: A227785 A227786 A227787 * A227789 A227790 A227791


KEYWORD

nonn,easy


AUTHOR

Alex Ratushnyak, Sep 23 2013


STATUS

approved



