Electrical – multiple LEDs in series

The most efficient method to do this would be with a boost converter, preferably one that has current control. Hundreds of LED drivers which are essentially modified power ICs are available nowadays, including ones that operate from single alkaline cells down to 0.9 V e.g. the Micrel MIC2282 (for more look up "single cell led driver") which should be able to drive up to 33 V strings (~8 LEDs), though asking it do that from a single cell may be pushing it

In a previous question, I did actually recommend a power IC, the Linear LT1618 (not outwardly marketed as an LED driver, but an application schematic showed it as one)

Whatever you choose, powering (20) 20 mA LEDs from a single alkaline cell is probably not feasible just because the voltage will dip so low with that load it will undervolt most controllers. If you could use two, you'd probably be in business.

Five LEDs in series will have a total voltage requirement of about 10V. This is closest to your supply voltage, so you would wire two such series runs in parallel. Each series run should have a current limiting resistor. The following schematic represents one "panel":

^{simulate this circuit – Schematic created using CircuitLab}

Assuming all LEDs have a \$V_f\$ of 2V, the current-limiting resistor would drop the remaining 2V. Since you want 20 mA, the value of the resistor is easy to calculate using Ohm's law (R = E / I):

$$\frac{2}{0.02} = 100\,\Omega$$

You should determine what actual voltage drop your LEDs have, but this gets you close.

There are other things you may want to do, such as add some overvoltage protection. If you're running this from a motorcycle battery that's not also connected to, say, a motorcycle, you shouldn't have any problems. However the alternator on a motorcycle (if it's like a car) may bring the voltage up to 13.8~14.4 volts.