A013583 Smallest positive number that can be written as sum of distinct Fibonacci numbers in n ways.

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

Offset: 1

Author

Marjorie Bicknell-Johnson (marjohnson(AT)earthlink.net)

Keywords

• nonn
• look

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.

Examples

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..5000
• 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.
• Petra Kocábová, Zuzana Masáková and Edita Pelantová, Integers with a maximal number of Fibonacci representations, RAIRO-Theor. Inf. Appl., Volume 39, Number 2, April-June 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], 2003-2015.

Crossrefs

Least inverse of A000119. Cf. A046815, A083853.

Formula

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

Extensions

Additional terms from Jeffrey Shallit

Extended to 600 terms by Daniel C. Fielder

Entries rechecked by David W. Wilson, Jun 18 2003