Long Timing with a 555 IC

There is a graph in the following link (labelled Monostable Nomograph) that allows you to pick any combination of resistance and capacitance that achieves the time you want:

https://www.electronics-tutorials.ws/waveforms/555_timer.html

Time = 1.1 x R x C

C = T / (1.1 x R)

For example if you want 52 seconds, and you pick R to be 1MOhm, then C is about 47 uf.

If you need to tweek the duty cycle (to get 3 offs for 1 on), you need a bit of extra components.

I have found speedy examples, no slow ones. Checking if I have a 555 in my bin ...

So I did not find an NE555 but LTSpice has a model.

I've replicated this design from All About Circuits (the article discusses several options);

R3 and R4 are the 500K potentiometer of their schematic.

This simulation could be used to find a good combinations of Rs and Cs, if you don't want to do the maths.

Changing R3 to 100K and R4 to 400K gives a very different duty cycle.

With a 100µ capacitor, 150K and 330K (E12 resistors somewhat close to on-off-off-off):

I've got some LM555, so I thought I'd try your last circuit (the 150k/330k one). I couldn't find a 100uF capacitor, so I'm using two 47uF tants in parallel. I'm using a 6V supply for this, like in your simulation. The waveforms look like this (yellow is the output, blue is the voltage on the capacitor)

The first timing interval is longer because the capacitor has to climb from zero rather than bobbing up and down between the two thresholds.

With the bipolar part [the CMOS variants may well be different], the upper output level doesn't go to the rail and moves around quite a bit with varying loads, and that affects the timing quite a bit. The original device was intended to have TTL output levels on 5V, so the low level is a saturated transistor, but the high will be some other kind of arrangement under the supply rail. On the above waveform, you can see it moving under the influence of the charging current. I've not seen the timing done like this from the output before, but then all the material on 555s I have predates the CMOS devices.

If I change your 150k to a 68k, I get this

which is closer to the mark-space ratio you have, though the period is shorter

One thing to be wary of, if the resistor values go too high, is capacitor leakage. If the charging current gets to be of the same order as the capacitor leakage plus the input bias currents, then obviously the capacitor won't then charge.