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A080804 Least number of connected subgraphs of the binary cube GF(2)^n such that every vertex of GF(2)^n lies in at least one of the subgraphs and no two vertices lie in the same set of subgraphs (such a collection is called an identifying set). 7
1, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n-1) is also the minimum number of matches in a tournament to fairly determine the best two players from n >= 2 contestants. For example, a(8-1) = a(7) = 9 matches are required to determine the best two players from 8 participants. See Steinhaus (1983). - Hugo Pfoertner, Dec 13 2022
REFERENCES
Hugo Steinhaus, Mathematical Snapshots, Third American Edition, Oxford University Press, New York, 1983, pp 54-55.
LINKS
Petri Rosendahl, On the identification problems in products of cycles, Discrete Mathematics, Volume 275, Issue 1, January 2004, pp 277-288.
FORMULA
a(n) = n + floor(log_2(n)).
MATHEMATICA
A080804[n_]:=n+Floor[Log2[n]]; Array[A080804, 100] (* Paolo Xausa, Sep 26 2023 *)
CROSSREFS
Second column of A360495.
Sequence in context: A039093 A085925 A107907 * A164386 A111909 A184010
KEYWORD
easy,nonn
AUTHOR
Pete Rosendahl (perosen(AT)utu.fi), Mar 26 2003
EXTENSIONS
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003
STATUS
approved

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Last modified April 17 12:12 EDT 2024. Contains 371763 sequences. (Running on oeis4.)