Let $a_{i}\in\{0,1,2,3,4,5,6,7,8,9\}, (i=1,2,\cdots,n,\cdots)$, and such that $$a_{n}\equiv \lfloor n\sin{n}\rfloor\pmod {10}$$
I conjecture : $\qquad 0.a_{1}a_{2}a_{3}\cdots a_{n}\cdots$ is rational number?
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1Do the decimals repeat? – Simply Beautiful Art Dec 22 '16 at 01:46
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@SimpleArt Yes.It's it – math110 Dec 22 '16 at 01:47
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5Why do you conjecture that this is rational? I would think it is not, as rationality is equivalent to this sequence being eventually periodic, but $\sin(n)$ is not periodic (as a function of integers) and $n\sin(n)$ looks even less periodic. – Milo Brandt Dec 22 '16 at 02:13