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Search: id:A013583
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| A013583 |
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Smallest positive number that can be written as sum of distinct Fibonacci numbers in n ways. |
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+0
7
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| 1, 3, 8, 16, 24, 37, 58, 63, 97, 105, 152, 160, 168, 249, 257, 270, 406, 401, 435, 448, 440, 647, 1011, 673, 723, 715, 1066, 1058, 1050, 1092, 1160, 1147, 1694, 1155, 1710, 1702, 2647, 1846, 1765, 1854, 2736, 1867, 2757, 2744, 2841, 2990, 2752, 2854, 2985, 3019, 4511, 3032, 6967, 4456, 3024, 4477, 4616, 4451, 7349, 4629, 7218, 4917, 4621, 4854, 4904, 7179, 7166, 4896, 7200, 7247, 7310, 7213, 7831, 8187, 7488, 7205, 11614, 7480, 7815, 7857, 7925, 11593, 18154, 7912, 11813, 11682, 11653
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Smallest nonnegative number that can be written as sum of distinct Fibonacci numbers in n ways would be the same, except starting with 0.
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REFERENCES
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Marjorie Bicknell-Johnson and Daniel C. Fielder, "The Least Number Having 331 Representations as a Sum of Distinct Fibonacci Numbers," Fibonacci Quarterly 39(2001), pp. 455-461.
Daniel C. Fielder and Marjorie Bicknell-Johnson, "The First 330 Terms of Sequence A013583", Fibonacci Quarterly 39 (2001), pp. 75-84.
Paul K. Stockmeyer, "A Smooth Tight Upper Bound for the Fibonacci Representation Function R(N)", Fibonacci Quarterly, Volume 46/47, Number 2, May 2009. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 04 2009]
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..5000
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FORMULA
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A000119(a(n)) = n (for n>1).
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EXAMPLE
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1 = 1; 3 = 3 = 2 + 1; 8 = 8 = 5 + 3 = 5 + 2 + 1.
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CROSSREFS
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Least inverse of A000119. Cf. A046815, A083853.
Sequence in context: A136532 A030417 A123979 this_sequence A122794 A115006 A122796
Adjacent sequences: A013580 A013581 A013582 this_sequence A013584 A013585 A013586
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KEYWORD
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nonn
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AUTHOR
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Marjorie Bicknell-Johnson (marjohnson(AT)earthlink.net)
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EXTENSIONS
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Additional terms from Jeffrey Shallit (shallit(AT)graceland.uwaterloo.ca); extended to 600 terms by Daniel C. Fielder
Entries rechecked by David W. Wilson, Jun 18 2003
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