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wu :: forums    riddles    medium (Moderators: Grimbal, towr, Icarus, SMQ, Eigenray, ThudnBlunder, william wu)    Same Leading Digit « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Same Leading Digit  (Read 616 times) ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Same Leading Digit   « on: Sep 5th, 2004, 7:04am » Quote Modify When n = 0 2n = 1 5n = 1 (Same leading digit)   When n = 5 2n = 32 5n = 3125 (Same leading digit)   Can you find any more such examples?   « Last Edit: Sep 5th, 2004, 7:07am by ThudnBlunder » IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Barukh Uberpuzzler     Gender: Posts: 2276 Re: Same Leading Digit   « Reply #1 on: Sep 5th, 2004, 9:30am » Quote Modify n=15. IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Same Leading Digit   « Reply #2 on: Sep 5th, 2004, 12:41pm » Quote Modify :: searching up to n = 200   n, 2n, 5n   0, 1, 1   5, 32, 3125   15, 32768, 30517578125   78, 302231454903657293676544, 3308722450212110699485634768279851414263248443603515625   88, 309485009821345068724781056, 32311742677852643549664402033982923967414535582065582275390625   98, 316912650057057350374175801344, 315544362088404722164691426113114491869282574043609201908111572265625   108, 324518553658426726783156020576256, 308148791101957736488956470813588370966096263714462111238390207290649414 0625   118, 332306998946228968225951765070086144, 300926553810505602039996553528894893521578382533654405506240436807274818 42041015625   181, 3064991081731777716716694054300618367237478244367204352, 326265223399926226335514705462827377785058212903448327387931822773486162 2298743113611448063426934140807134099304676055908203125   191, 3138550867693340381917894711603833208051177722232017256448, 318618382226490455405776079553542361118220911038523757214777170677232580 30261163218861797494403653718819668938522227108478546142578125 :: « Last Edit: Sep 5th, 2004, 12:44pm by towr » IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Barukh Uberpuzzler     Gender: Posts: 2276 Re: Same Leading Digit   « Reply #3 on: Sep 6th, 2004, 4:25am » Quote Modify It is not difficult to see that there are infinitely many such numbers.   Using continued fractions one can find fairly big examples without actual search (but of course not all such numbers!).   Here're a few: 14369, 56408, 127185, 3053508, 22349997. 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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