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A214981
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Number of terms in the greedy Lucas-and-Fibonacci representations of 1,2,...,n; partial sums of A214973.
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4
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1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 16, 17, 19, 21, 23, 25, 26, 28, 30, 31, 33, 35, 37, 39, 41, 44, 46, 47, 49, 51, 53, 55, 56, 58, 60, 62, 64, 66, 69, 71, 73, 76, 79, 81, 84, 85, 87, 89, 91, 93, 95, 98, 100, 101, 103, 105, 107, 109, 111, 114, 116, 118, 121, 124
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OFFSET
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1,2
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COMMENTS
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For comparison with Zeckendorf (Fibonacci) representations, it is conjectured that the limit of A179180(n)/A214981(n) exists and is between 1.2 and 1.4.
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LINKS
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EXAMPLE
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The basis is B = (1,2,3,4,5,7,8,11,13,18,21,29,34,47,55,...), composed of Fibonacci numbers and Lucas numbers. Representations of positive integers using the greedy algorithm on B:
n repres. # terms a(n)
1 1 1 1
2 2 1 2
3 3 1 3
4 4 1 4
5 5 1 5
6 5+1 2 7
7 7 1 8
8 8 1 9
9 8+1 2 11
10 8+2 2 13
27 21+5+1 3 44
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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