A260998 Maximal size of a subset of Z_n with distinct sums of pairs (of distinct elements).
1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10
Offset: 1
Keywords
Links
- Fausto A. C. Cariboni, Table of n, a(n) for n = 1..254
- Fausto A. C. Cariboni, S_2-sets that yield a(n) for n = 2..254, Mar 24 2018.
- 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]
- 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.
Formula
By the pigeonhole principle, C(a(n),2) <= n, yielding upper bound a(n) <= floor((1+sqrt(8*n+1))/2). - Rob Pratt, Nov 27 2017
Extensions
a(1)-a(90) from H. Haanpaa, A. Huima and Patric R. J. Östergård (see link), Nov 08 2000
a(1)-a(90) confirmed by Fausto A. C. Cariboni, Nov 09 2017