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Consider the sequence $$s_n:=frac(n^{\sqrt{2}})$$ $n=1,2,3,\cdots$

Is $s_n$ dense in $[0,1]$ ?

The number $$12230575^{\sqrt{2}}$$ is almost an integer, but I do not know whether we can get arbitary close to an integer. And even this would not show that we can get arbitary near to any given number $t\in [0,1]$. For example $$frac(4555670^{\sqrt{2}})$$ is very near to $0.\overline{676}$. Any ideas ?

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    @PatrickStevens Doesn't $\lfloor\cdot\rfloor$ usually denote the floor function? – 2017-02-20
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    "frac" is the fractional part : $frac(x)=x-\lfloor x\rfloor$ – 2017-02-20

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