[go: up one dir, main page]

login
A058992
Gossip Problem: there are n people and each of them knows some item of gossip not known to the others. They communicate by telephone and whenever one person calls another, they tell each other all that they know at that time. How many calls are required before each gossip knows everything?
7
0, 1, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124
OFFSET
1,3
COMMENTS
The sequence (for n>=1) refers to the famous "nine dots puzzle" as well. It represents the minimum number of straight lines that you need to fit the centers of n^2 dots (without lifting the pencil from the paper). - Marco Ripà, Apr 01 2013
REFERENCES
R. Tijdeman, On a telephone problem. Nieuw Arch. Wisk. (3) 19 (1971), 188-192. Math. Rev. 49 #7151
LINKS
B. Baker and R. Shostak, Gossips and Telephones, Discrete Mathematics 2 (1972) 191-193. Math. Rev. 46 # 68.
R. T. Bumby, A problem with telephones, SIAM J. Alg. Disc. Meth. 2 (1981) 13-18. Math. Rev. 82f:05083.
A. Hajnal, E. C. Milner and E. Szemeredi, A cure for the telephone disease Canad. Math. Bull. 15 (1972), 447-450. Math. Rev. 47 #3184.
D. J. Kleitman and J. B. Shearer, Further Gossip Problems, Discrete Mathematics 30 (1980), 151-156. Math. Rev. 81d:05068.
T. Sillke, References
T. Sillke, Proofs
Wikipedia, nine dots puzzle
FORMULA
a(n) = 2n - 4 for n >= 4.
G.f.: x^2*(1+x-x^2+x^3)/(1-x)^2. - Colin Barker, Jun 07 2012
MATHEMATICA
Join[{0, 1, 3}, NestList[#+2&, 4, 60]] (* Harvey P. Dale, Apr 01 2012 *)
PROG
(PARI) a(n)=if(n>3, 2*n-4, [0, 1, 3][n]) \\ Charles R Greathouse IV, Feb 10 2017
CROSSREFS
Cf. A007456.
Sequence in context: A184736 A173472 A334905 * A051755 A092535 A215476
KEYWORD
easy,nonn,nice
AUTHOR
Torsten Sillke (torsten.sillke(at)lhsystems.com), Jan 17 2001
STATUS
approved