OFFSET
1,2
COMMENTS
From Fausto A. C. Cariboni, Oct 08 2017: (Start)
Lexicographically first basis that yields a(n) for n=16:
a(16) = 252 from {0,1,2,4,32,47,54,65,94,120,128,145,169,196,217,240}
(End)
From Fausto A. C. Cariboni, Mar 12 2018: (Start)
Lexicographically first basis that yields a(n) for n=17:
a(17) = 255 from {0,1,2,4,8,16,27,32,54,64,99,108,128,141,177,198,216}
(End)
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, arXiv:1705.07444 [math.NT], May 2017. See Problem C.61.
R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs, SIAM J. Algebraic and Discrete Methods, 1 (1980), 382-404.
R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs
H. Haanpaa, A. Huima and Patric R. J. Östergård, Sets in Z_n with Distinct Sums of Pairs, in Optimal discrete structures and algorithms (ODSA 2000). Discrete Appl. Math. 138 (2004), no. 1-2, 99-106.
H. Haanpaa, A. Huima and Patric R. J. Östergård, Sets in Z_n with Distinct Sums of Pairs, in Optimal discrete structures and algorithms (ODSA 2000). Discrete Appl. Math. 138 (2004), no. 1-2, 99-106. [Annotated scanned copies of four pages only from preprint of paper]
Z. Skupien, A. Zak, Pair-sums packing and rainbow cliques, in Topics In Graph Theory, A tribute to A. A. and T. E. Zykovs on the occasion of A. A. Zykov's 90th birthday, ed. R. Tyshkevich, Univ. Illinois, 2013, pages 131-144, (in English and Russian) [gives the term 183].
EXAMPLE
a(4)=6: the set {0,1,2,4} is such a subset of Z_6, since 0+1, 0+2, 0+4, 1+2, 1+4 and 2+4 are all distinct in Z_6; also, no such 4-element set exists in any smaller cyclic group.
CROSSREFS
KEYWORD
nonn,nice,more
AUTHOR
EXTENSIONS
More terms and comments from Harri Haanpaa (Harri.Haanpaa(AT)hut.fi), Nov 01 2000
a(16) from Fausto A. C. Cariboni, Oct 08 2017
a(17) from Fausto A. C. Cariboni, Mar 12 2018
STATUS
approved