

A013583


Smallest positive number that can be written as sum of distinct Fibonacci numbers in n ways.


7



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
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OFFSET

1,2


COMMENTS

Smallest nonnegative number that can be written as sum of distinct Fibonacci numbers in n ways would be the same, except starting with 0.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..5000
Marjorie BicknellJohnson and Daniel C. Fielder, The Least Number Having 331 Representations as a Sum of Distinct Fibonacci Numbers, Fibonacci Quarterly 39(2001), pp. 455461.
Daniel C. Fielder and Marjorie BicknellJohnson, The First 330 Terms of Sequence A013583, Fibonacci Quarterly 39 (2001), pp. 7584.
Petra Kocábová, Zuzana Masáková and Edita Pelantová, Integers with a maximal number of Fibonacci representations, RAIROTheor. Inf. Appl., Volume 39, Number 2, AprilJune 2005.
Paul K. Stockmeyer, A Smooth Tight Upper Bound for the Fibonacci Representation Function R(N), Fibonacci Quarterly, Volume 46/47, Number 2, May 2009.
F. V. Weinstein, Notes on Fibonacci Partitions, arXiv:math/0307150 [math.NT], 20032015.


FORMULA

A000119(a(n)) = n (for n>1).


EXAMPLE

1 = 1; 3 = 3 = 2 + 1; 8 = 8 = 5 + 3 = 5 + 2 + 1.


CROSSREFS

Least inverse of A000119. Cf. A046815, A083853.
Sequence in context: A190450 A188012 A123979 * A122794 A225268 A211481
Adjacent sequences: A013580 A013581 A013582 * A013584 A013585 A013586


KEYWORD

nonn,look


AUTHOR

Marjorie BicknellJohnson (marjohnson(AT)earthlink.net)


EXTENSIONS

Additional terms from Jeffrey Shallit
Extended to 600 terms by Daniel C. Fielder
Entries rechecked by David W. Wilson, Jun 18 2003


STATUS

approved



