cp's OEIS Frontend

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

%I A007456 #22 Jun 17 2022 12:26:02
%S A007456 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,
%T A007456 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,
%U A007456 8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8
%N A007456 Number of days required to spread gossip to n people.
%C A007456 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.
%C A007456 a(A240277(n)) = n and a(m) < n for m < A240277(n). - _Reinhard Zumkeller_, Apr 03 2014
%D A007456 D. Shasha, Gossiping Defenders, The Puzzling Adventures of Dr. Ecco, pp. 62-4;156 W. H. Freeman NY 1988.
%H A007456 T. D. Noe, <a href="/A007456/b007456.txt">Table of n, a(n) for n = 1..10000</a>
%H A007456 C. Kenneth Fan, Bjorn Poonen and George Poonen, <a href="http://www.jstor.org/stable/2691050">How to spread rumors fast</a>, Mathematics Magazine 70 (Feb, 1997), pp. 40-42.
%H A007456 I. Peterson, <a href="https://web.archive.org/web/20130702062252/http://www.maa.org/mathland/mathland_3_17.html">Spreading Rumors</a>, MathLand, March 17, 1997.
%F A007456 a(1) = 0; for n >= 2, a(n) = floor(log_2(n-1)) + ((n-2) mod 2) + 1.
%F A007456 G.f.: -1 + (1/(1-z))*(1/(1+z) + Sum_{k>=0} z^(2^k)). - _Ralf Stephan_, Apr 06 2003
%t A007456 Join[{0}, Table[Floor[Log[2, n - 1]] + Mod[n - 2, 2] + 1, {n, 2, 100}]] (* _T. D. Noe_, Mar 16 2012 *)
%o A007456 (Haskell)
%o A007456 a007456 1 = 0
%o A007456 a007456 n = a000523 (n - 1) + mod n 2 + 1
%o A007456 -- _Reinhard Zumkeller_, Apr 03 2014
%Y A007456 Cf. A160464, A043529.
%Y A007456 Cf. A000523.
%K A007456 nonn,nice,easy
%O A007456 1,3
%A A007456 Alex Graesser (AlexG(AT)sni.co.za)
%E A007456 More terms from _David W. Wilson_
%E A007456 Formulae corrected by _Johannes W. Meijer_, May 15 2009