I need a circuit which outputs a LOW level on power-up state. INPUT stays LOW. Once INPUT goes HIGH I need to run a delay which will set OUTPUT to HIGH after timed delay T (which is measured in seconds, should be configurable within 1-20s, accuracy aren't important). OUTPUT should stay HIGH until complete power-off. Rest INPUT level transitions are ignored. Like this:
The only difference that button LOW level triggers transition, but it can be inverted with other inverter IO on same 4584 I guess.
Will this work in real hardware or maybe someone could suggest a better circuit for my needs?
EDIT: Based on @elliot-alderson answer, I've modified my schematics to make sure both flip-flops will output LOW level at power on and no inputs are floating: I've also changed button position to simulate original low-to-high transition input as drawn on my 1st diagram.
How about this version?