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wu :: forums    riddles    medium (Moderators: towr, Icarus, ThudnBlunder, Grimbal, william wu, SMQ, Eigenray)    fibonacci iteration « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: fibonacci iteration  (Read 1164 times) Christine Full Member     Posts: 159 fibonacci iteration   « on: Mar 26th, 2014, 10:12am » Quote Modify If you take any Fibonacci number (except 1, 13)   find the sum of the squares of its digits, and then repeat; you will come to 89   why is that? IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: fibonacci iteration   « Reply #1 on: Mar 26th, 2014, 10:39am » Quote Modify It's true for 856929 of the first million non-negative integers, so it's not special to Fibonacci numbers.   Also, it's not true for quite a few Fibonacci numbers, e.g.: 17 :  2584 18 :  4181 24 :  75025 31 :  2178309 32 :  3524578 44 :  1134903170 49 :  12586269025 82 :  99194853094755497 83 :  160500643816367088 86 :  679891637638612258 92 :  12200160415121876738 105 :  6356306993006846248183 108 :  26925748508234281076009 114 :  483162952612010163284885 116 :  1264937032042997393488322 121 :  14028366653498915298923761 125 :  96151855463018422468774568 129 :  659034621587630041982498215 131 :  1725375039079340637797070384 132 :  2791715456571051233611642553 133 :  4517090495650391871408712937 142 :  343358302784187294870275058337   In fact, it's about the same fraction as for regular integers, again pointing to Fibonacci numbers not being special. « Last Edit: Mar 26th, 2014, 10:57am by towr » IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Christine Full Member     Posts: 159 Re: fibonacci iteration   « Reply #2 on: Mar 26th, 2014, 11:10am » Quote Modify Thanks. I've just looked at prime curios! page http://primes.utm.edu/curios/page.php/89.html   One entry, it reads: Hugo Steinhaus (1887-1972) proved that if you take any positive integer, find the sum of the squares of its digits, and then repeat; that you will either come to 1 or the cyclic sequence 145, 42, 20, 4, 16, 37, 58, 89.   It doesn't mention about percentage of getting a 89 or any percentages of these numbers IP Logged rmsgrey Uberpuzzler     Gender: Posts: 2872 Re: fibonacci iteration   « Reply #3 on: Mar 27th, 2014, 5:11am » Quote Modify http://en.wikipedia.org/wiki/Happy_numbers seems relevant IP Logged Christine Full Member     Posts: 159 Re: fibonacci iteration   « Reply #4 on: Mar 30th, 2014, 1:23pm » Quote Modify thanks 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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