Can anyone spot the logic behind this sequence?
series/letter.count.convergence New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
Can anyone spot the logic behind this sequence? 1, 3, 5, 4, 4, 4, 4 ... -- Paul Cockburn <paul@mazarbul.demon.co.uk>, December 1997 And this one? 1, 2, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5 ... -- Nick Wedd <Nick@maproom.demon.co.uk> [ Editor: Cockburn asked about "these sequences"; only this one is quoted in the collected material. The second is Wedd's reply. ]
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[ Editor: each term is the number of letters in the name of the previous term, in English (one, three, five, four, ...) and in French (un, deux, quatre, six, trois, cinq, ...); the replies take this for granted. ] How do different languages behave? English: converges to 4. Spanish: converges to 4,6 cycle. French: converges to 3,5,4,6 cycle. German: converges to 4. Hebrew: converges to 4. Is there any language with more than one cycle? -- David Grabiner <grabiner@math.lsa.umich.edu> Italian: converges to 3. Russian can either enter a cycle of 4,6,5 or settle on 11. Swedish settles on either 3 or 4 (tre, fyra). Esperanto can end on 2, 3 or 4 (du, tri, kvar). -- Fred W. Helenius <fredh@ix.netcom.com> Dutch: 1, 3, 4, 4, 4 2, 4, 4, 4, 4 3, 4 4, 4 5, 3 6, 3 7, 5 8, 4 9, 5 10, 4 11, 3 12, 6 13, 7 14, 8 15, 7 Looks like it converges on 4 as well... -- Christ van Willegen <j.h.christ@spc.nl>, December 1997