Maybe I should have included this small note previously, (I had figured it was a small typo or something) but, x cos(x) / (2pi) does not actually produce intege

Maybe I should have included this small note previously, (I had figured it was a small typo or something) but, x cos(x) / (2pi) does not actually produce integers for integer values of x (other than for x=0) . I imagine what you mean is more along the lines of x cos(pi x) ? However, this does not produce the sequence -1,1,-2,2,... either. Rather, it produces -1,2,-3,4,... Which, again, can be produced with (-1)^x • x , not using any trig functions. I suppose one might object that (-1)^x doesn’t have real values for non-integer values of x, but I’m not sure why that should be super relevant to the “what does this sequence of numbers indicate”. If you want a formula for -1,1,-2,2,-3,3,... then, well, there’s the one I posted earlier, using the floor or ceiling function, or if one wanted one could come up with something for it using multiple uses of trig functions, but it would be inelegant.