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

%I A013583 #36 Jan 05 2025 19:51:34
%S A013583 1,3,8,16,24,37,58,63,97,105,152,160,168,249,257,270,406,401,435,448,
%T A013583 440,647,1011,673,723,715,1066,1058,1050,1092,1160,1147,1694,1155,
%U A013583 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
%N A013583 Smallest positive number that can be written as sum of distinct Fibonacci numbers in n ways.
%C A013583 Smallest nonnegative number that can be written as sum of distinct Fibonacci numbers in n ways would be the same, except starting with 0.
%H A013583 Charles R Greathouse IV, <a href="/A013583/b013583.txt">Table of n, a(n) for n = 1..5000</a>
%H A013583 Marjorie Bicknell-Johnson and Daniel C. Fielder, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/39-5/bicknell.pdf">The Least Number Having 331 Representations as a Sum of Distinct Fibonacci Numbers</a>, Fibonacci Quarterly 39(2001), pp. 455-461.
%H A013583 Daniel C. Fielder and Marjorie Bicknell-Johnson, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/39-1/fielder.pdf">The First 330 Terms of Sequence A013583</a>, Fibonacci Quarterly 39 (2001), pp. 75-84.
%H A013583 Petra Kocábová, Zuzana Masáková and Edita Pelantová, <a href="http://dx.doi.org/10.1051/ita:2005022">Integers with a maximal number of Fibonacci representations</a>, RAIRO-Theor. Inf. Appl., Volume 39, Number 2, April-June 2005.
%H A013583 Paul K. Stockmeyer, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/46_47-2/Stockmeyer.pdf">A Smooth Tight Upper Bound for the Fibonacci Representation Function R(N)</a>, Fibonacci Quarterly, Volume 46/47, Number 2, May 2009.
%H A013583 F. V. Weinstein, <a href="http://arxiv.org/abs/math/0307150">Notes on Fibonacci Partitions</a>, arXiv:math/0307150 [math.NT], 2003-2015.
%F A013583 A000119(a(n)) = n (for n>1).
%e A013583 1 = 1; 3 = 3 = 2 + 1; 8 = 8 = 5 + 3 = 5 + 2 + 1.
%Y A013583 Least inverse of A000119. Cf. A046815, A083853.
%K A013583 nonn,look
%O A013583 1,2
%A A013583 Marjorie Bicknell-Johnson (marjohnson(AT)earthlink.net)
%E A013583 Additional terms from _Jeffrey Shallit_
%E A013583 Extended to 600 terms by Daniel C. Fielder
%E A013583 Entries rechecked by _David W. Wilson_, Jun 18 2003