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wu :: forums    riddles    easy (Moderators: Grimbal, william wu, ThudnBlunder, Icarus, Eigenray, SMQ, towr)    sequence « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: sequence  (Read 517 times) puzzlecracker Senior Riddler Men have become the tools of their tools     Gender: Posts: 319 sequence   « on: Feb 21st, 2005, 9:38am » Quote Modify what is the next number in the sequence?   1, 2, 5, 14, 41, ___ IP Logged While we are postponing, life speeds by ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: sequence   « Reply #1 on: Feb 21st, 2005, 10:01am » Quote Modify Just out of curiosity, where did you get this puzzle? IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. rmsgrey Uberpuzzler     Gender: Posts: 2873 Re: sequence   « Reply #2 on: Feb 21st, 2005, 10:27am » Quote Modify 122 IP Logged ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: sequence   « Reply #3 on: Feb 21st, 2005, 11:01am » Quote Modify on Feb 21st, 2005, 10:27am, rmsgrey wrote: 122 Not worth hiding, eh? IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Sameer Uberpuzzler Pie = pi * e     Gender: Posts: 1261 Re: sequence   « Reply #4 on: Feb 21st, 2005, 12:48pm » Quote Modify ::   a(n)=a(n-1)*3-1   giving 122 :: « Last Edit: Feb 21st, 2005, 12:49pm by Sameer » IP Logged "Obvious" is the most dangerous word in mathematics. --Bell, Eric Temple Proof is an idol before which the mathematician tortures himself. Sir Arthur Eddington, quoted in Bridges to Infinity puzzlecracker Senior Riddler Men have become the tools of their tools     Gender: Posts: 319 Re: sequence   « Reply #5 on: Feb 21st, 2005, 1:14pm » Quote Modify on Feb 21st, 2005, 10:01am, THUDandBLUNDER wrote: Just out of curiosity, where did you get this puzzle?   some interview I think...       have you also seen this question? IP Logged While we are postponing, life speeds by JocK Uberpuzzler     Gender: Posts: 877 Re: sequence   « Reply #6 on: Feb 21st, 2005, 2:35pm » Quote Modify The next number in the sequence 1, 2, 5, 14, 41, ?   That's easy: 122. And the number thereafter is 366.     IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: sequence   « Reply #7 on: Feb 22nd, 2005, 1:09am » Quote Modify on Feb 21st, 2005, 1:14pm, puzzlecracker wrote:   have you also seen this question? Not this exact question. But I think it is too easy, even for Easy. T(n) = 3T(n-1) - 1   on Feb 21st, 2005, 2:35pm, JocK wrote: And the number thereafter is 366. Only during a leap year.     « Last Edit: Feb 22nd, 2005, 1:26am by ThudnBlunder » IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. rmsgrey Uberpuzzler     Gender: Posts: 2873 Re: sequence   « Reply #8 on: Feb 22nd, 2005, 5:42am » Quote Modify on Feb 21st, 2005, 11:01am, THUDandBLUNDER wrote: Not worth hiding, eh? Not while the hide tags are still offline - and a naked answer like that doesn't give much away - but stil allows others to check their guesses against mine IP Logged JocK Uberpuzzler     Gender: Posts: 877 Re: sequence   « Reply #9 on: Feb 22nd, 2005, 11:57am » Quote Modify on Feb 22nd, 2005, 1:09am, THUDandBLUNDER wrote:   Only during a leap year.     No, always... Obviously the sequence asked for is the sequence defined by the property that its generating function is the same as its continued fraction:   1, 2, 5, 14, 41, 122, 366, 1103, 3332, 10078, 30503, 92360, 279722, 847283   on Feb 22nd, 2005, 1:09am, THUDandBLUNDER wrote: [..] I think it is too easy, even for Easy.   I think it is too hard for Easy..! « Last Edit: Feb 22nd, 2005, 2:43pm by JocK » IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: sequence   « Reply #10 on: Feb 23rd, 2005, 6:24am » Quote Modify on Feb 22nd, 2005, 11:57am, JocK wrote: No, always... Obviously the sequence asked for is the sequence defined by the property that its generating function is the same as its continued fraction: Yes, a typically perplexing puzzlecracker poser.     . « Last Edit: Feb 23rd, 2005, 6:25am by ThudnBlunder » IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Sjoerd Job Postmus Full Member     Posts: 228 Re: sequence   « Reply #11 on: Mar 4th, 2005, 5:45am » Quote Modify on Feb 21st, 2005, 2:35pm, JocK wrote: The next number in the sequence 1, 2, 5, 14, 41, ?   That's easy: 122. And the number thereafter is 366.     This makes me wonder how you arrive to 366.   since someone stated that a(n) = a(n-1)*3 - 1, the first list follows logically, up to the 122. The 366 however, does not follow logically. When I fill in 122*3 - 1, 365 follows, not 366. Following the formula, the next would be 1094.   How did you derive your own answer, as I do not understand. IP Logged rmsgrey Uberpuzzler     Gender: Posts: 2873 Re: sequence   « Reply #12 on: Mar 4th, 2005, 6:51am » Quote Modify on Mar 4th, 2005, 5:45am, Sjoerd Job Postmus wrote: This makes me wonder how you arrive to 366.   since someone stated that a(n) = a(n-1)*3 - 1, the first list follows logically, up to the 122. The 366 however, does not follow logically. When I fill in 122*3 - 1, 365 follows, not 366. Following the formula, the next would be 1094.   How did you derive your own answer, as I do not understand. He "explained" his reasoning in a later post: on Feb 22nd, 2005, 11:57am, JocK wrote: No, always... Obviously the sequence asked for is the sequence defined by the property that its generating function is the same as its continued fraction:   1, 2, 5, 14, 41, 122, 366, 1103, 3332, 10078, 30503, 92360, 279722, 847283     I think it is too hard for Easy..! Mathworld is a good source for definitions of mathematical terms: Generating Function and Continued Fraction IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: sequence   « Reply #13 on: Mar 4th, 2005, 8:41am » Quote Modify You can also have a look at: http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cg i?Anum=A088355 IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------=> easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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