Equivalent conditions for the $n$ th element of the Beatty sequence $B_{\sqrt{2}}$ being even

preprint2022arXivOpen access

We provide equivalent conditions for the $n$ th element of the Beatty sequence $B_{\sqrt{2}}$ being even. In particular, we show that the integer sequences A090892 and A120752 in the OEIS are essentially identical.

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Equivalent conditions for the $n$ th element of the Beatty sequence $B_{\sqrt{2}}$ being even

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Equivalent conditions for the nnnth element of the Beatty sequence B2B_{\sqrt{2}}B2​​ being even

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Equivalent conditions for the $n$ th element of the Beatty sequence $B_{\sqrt{2}}$ being even