Almost 20 years ago, de Vries proposed a recursive equation for the fine structure constant α that depends only on the mathematical constants e and π. It gives a value for 1/α = 137.0359990958. By applying the term α/(2π) in a geometric series, this equation has the flavour of mainstream physics (see Schwinger-Dyson series on calculating the electron's g-factor), which in combination with the agreement with the experimentally found value is probably the reason why this formula, unlike many other numerology attempts, is not forgotten.The starting point and core element of this equation is the term 1/e^(π^2/2). Despite interesting approaches, it has not yet been possible to give this term an unequivocal physical meaning. So I thought it worthwhile to investigate the proximity of this value to the closest power-of-two value, i.e. 128. This resulted from the considerations I made in the previous works, where I (among many others) became aware of the importance of the number 2^128 as a link between the order of magnitude of the elementary particles and the universe.Finally, another equation for α was obtained, which is roughly equivalent in complexity to the de Vries equation, depends only on π and 128, and whose result differs from the de Vries result by only about 2^10^-10.It was during my playing around with the numerical values that I found the literature that told me that at extremely high energies the fine structure "constant" increases to the value of about 1/128. So I saw another reason to publish these number juggleries. Here they are.