A007456 Number of days required to spread gossip to n people.

0, 1, 3, 2, 4, 3, 4, 3, 5, 4, 5, 4, 5, 4, 5, 4, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8

Offset

1,3

Comments

On the first day, each gossip has his own tidbit. On each successive day, disjoint pairs of gossips may share tidbits (over the phone). After a(n) days, all gossips have all tidbits.

a(A240277(n)) = n and a(m) < n for m < A240277(n). - Reinhard Zumkeller, Apr 03 2014

References

D. Shasha, Gossiping Defenders, The Puzzling Adventures of Dr. Ecco, pp. 62-4;156 W. H. Freeman NY 1988.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

C. Kenneth Fan, Bjorn Poonen and George Poonen, How to spread rumors fast, Mathematics Magazine 70 (Feb, 1997), pp. 40-42.

I. Peterson, Spreading Rumors, MathLand, March 17, 1997.

Formula

a(1) = 0; for n >= 2, a(n) = floor(log_2(n-1)) + ((n-2) mod 2) + 1.

G.f.: -1 + (1/(1-z))*(1/(1+z) + Sum_{k>=0} z^(2^k)). - Ralf Stephan, Apr 06 2003

Mathematica

Join[{0}, Table[Floor[Log[2, n - 1]] + Mod[n - 2, 2] + 1, {n, 2, 100}]] (* T. D. Noe, Mar 16 2012 *)

Prog

(Haskell)
a007456 1 = 0
a007456 n = a000523 (n - 1) + mod n 2 + 1
-- Reinhard Zumkeller, Apr 03 2014

Crossrefs

Cf. A160464, A043529.

Cf. A000523.

Sequence in context: A243289 A134559 A333773 * A316141 A119707 A377298

Adjacent sequences: A007453 A007454 A007455 * A007457 A007458 A007459

Keyword

nonn,nice,easy

Author

Alex Graesser (AlexG(AT)sni.co.za)

Extensions

More terms from David W. Wilson

Formulae corrected by Johannes W. Meijer, May 15 2009

Status

approved