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TOT 307 1991 Autumn A J4 a_{k+1}=3a_k^4+4a_k^3, NT

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June 9, 2024
number theoryDigitsrecurrence relation

Problem Statement

A sequence ana_n is determined by the rules a0=9a_0 = 9 and for any nonnegative kk, ak+1=3ak4+4ak3.a_{k+1}=3a_k^4+4a_k^3. Prove that a10a_{10} contains more than 10001000 nines in decimal notation.
(Yao)
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