Back in the beginning of July, I replaced the NP-BX1 battery in the RGB Piranha astable multivibrator with a 18650 lithium cell and a USB charge controller, then watched it blink for the next two weeks on the first charge:

However, the blinks looked … odd and some poking around with a Tek current probe showed the red and blue astables had locked together, so they blinked in quick succession. Alas, I don’t have a scope shot to prove it.
I built all three astables with the same parts, figuring the normal tolerance of electrolytic caps would make the astables run at slightly different rates, which they did at first.
This being a prototype, I just soldered a 1 µF cap onto the blue channel’s existing 10 µF cap:

You can barely make out the top of the additional 2.2 µF cap on the red channel, through the maze of components; now, they definitely have different periods.
Aaaand the scope shot to prove it:

The bottom trace shows the battery current at 10 mA/div. The first pulse, over on the left, has the red and blue LEDs firing in quick succession with some overlap, but they separate cleanly for their next pulses.
You don’t want to build a battery-powered astable from NPN transistors, because the 8 mA current between blinks is murderously high. In round numbers, each of the three LEDs blinks twice a second for 30 ms at 20 mA, so they average 3.6 mA, less than half the current required to keep the astables running between blinks. Over the course of 14 days, the circuit drew 11.6 mA × 336 hr = 3900 mA·h until the protection circuit shut it down.
The lead photo shows a harvested 18650 cell, but I started with a known-good Samsung 18650 cell rated at 2600 mA·h at a 0.2C = 520 mA rate to 2.75 V. It’s comforting to see more energy trickling out at a 0.005C rate!
I must conjure a holder with contacts for an 18650 cell, support for a trio of 2N7000 MOSFET astables, and some kind of weird spider with the RGB Piranha LED on the top. Even a harvested 18650 cell should last a couple of months with a much longer blink period (500 ms is much too fast), less LED current (this one is shatteringly bright), and a lower average current.
And, yeah, I’ve been misspelling “Piranha” for a while.
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