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?

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

Author

Torsten Sillke (torsten.sillke(at)lhsystems.com), Jan 17 2001

Keywords

• easy
• nonn
• nice

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

• T. D. Noe, Table of n, a(n) for n = 1..1000
• 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
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A007456.

Programs

Mathematica

Join[{0,1,3}, NestList[#+2&,4,60]] (* Harvey P. Dale, Apr 01 2012 *)

PARI

a(n)=if(n>3, 2*n-4, [0,1,3][n])  \\ Charles R Greathouse IV, Feb 10 2017

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