Almost integer - Wikipedia
In recreational mathematics, an almost integer (or near-integer) is any number that is not an integer but is very close to one. Almost integers may be considered interesting when they arise in some context in which they are unexpected.
Some examples of almost integers are high powers of the golden ratio ϕ = 1 + 5 2 ≈ 1.618 {\displaystyle \phi ={\frac {1+{\sqrt {5}}}{2}}\approx 1.618} , for example:
The fact that these powers approach integers is non-coincidental, because the golden ratio is a Pisot–Vijayaraghavan number.
The above examples can be generalized by the following sequences, which generate near-integers approaching Lucas numbers with increasing precision:
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