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donjar

Barisan naik/turun

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Sebuah barisan bilangan real $a_0, a_1, \dotsc$ disebut baik jika:


(i) $a_0$ bulat positif.


(ii) Untuk setiap $i$ bulat dipunyai $a_{i+1}=2a_i+1$ atau $a_{i+1}=\frac{a_i}{a_i+2}$.


(iii) Terdapat sebuah bilangan bulat positif $k$ sehingga $a_k=2014$.


 


Cari bilangan bulat $n$ terkecil sehingga terdapat barisan bilangan real baik $a_0, a_1, \dotsc$ dengan $a_n=2014$.


 


APMO 2015 no. 3 oleh Wang Wei Hua, Hong Kong


 


SPOILER BESAR



$n=60$ :v



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