Is \(\left\lfloor\dfrac{n!}{e}\right\rfloor,\ \forall n\in\mathbb{N}\) always even? or equivalently, is \(\dfrac{1}{2}\left\lfloor\dfrac{n!}{e}\right\rfloor,\ \forall n\in\mathbb{N}\) always an integer?🤔 🔗 https://www.youtube.com/watch?v=wrHxeHJDTk4&t=604s&ab_channel=MichaelPenn

#floorfunction #function #even #EulerNumber #Factorial #NaturalNumber #MichaelPenn

For fans of #integer #sequences that haven't seen it, check out https://en.wikipedia.org/wiki/Gijswijt's_sequence

Trivially described #sequence which contains every #NaturalNumber, but appearing at an insanely slow rate... first five appear at approx. indices \(\{1, 3,9,220, 10^{10^{23}}\}. \)

#math