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A007456
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Days required to spread gossip to n people.
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5
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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, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| On 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.
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REFERENCES
| Fan, C. Kenneth, Bjorn Poonen and George Poonen, How to spread rumors fast. Mathematics Magazine 70 (Feb, 1997), pp. 40-42.
D. Shasha, Gossiping Defenders, The Puzzling Adventures of Dr. Ecco, pp. 62-4;156 W. H. Freeman NY 1988.
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LINKS
| I. Peterson, Spreading Rumors, MathLand, March 17, 1997.
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FORMULA
| a(1) = 0; a(n) = [ log_2 (n-1) ] + ((n-2) mod 2) + 1 (n >= 2)
G.f.: 1/(1-z)*(sum(k>=0, z^(2^k))+1/(1+z))-1. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 06 2003
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CROSSREFS
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)
Cf. A160464 and A043529.
(End)
Sequence in context: A025509 A130079 A134559 * A119707 A052938 A140114
Adjacent sequences: A007453 A007454 A007455 * A007457 A007458 A007459
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KEYWORD
| nonn,nice,easy
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AUTHOR
| Alex Graesser (AlexG(AT)sni.co.za)
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net)
Formulae corrected by Johannes W. Meijer (meijgia(AT)hotmail.com), May 15 2009
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