A260999 Maximal size of a subset of Z_n with distinct sums of any two elements.

1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8

Offset

1,3

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 1..295

Fausto A. C. Cariboni, Sets that yield a(n) for n = 2..295, Jan 27 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)+1,2) <= n, yielding upper bound a(n) <= floor((-1+sqrt(8*n+1))/2). - Rob Pratt, Nov 27 2017

Crossrefs

Cf. A004135, A004136, A260998.

Sequence in context: A023967 A278163 A347635 * A090532 A003058 A000194

Adjacent sequences: A260996 A260997 A260998 * A261000 A261001 A261002

Keyword

nonn

Author

N. J. A. Sloane, Aug 10 2015

Extensions

More terms from Rob Pratt, Nov 27 2017

Status

approved