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A227789
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Sum of indices of Fibonacci numbers in Zeckendorf representation of n, assuming that the units place is Fibonacci(1).
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1
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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