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I would recommend to use the first version from wkarraker with the two LEDs in serial connection. Depending on the quality of the LEDs some of them might be lighter or dimmer if connected in parallel like in the second example picture. The current limiting resistor should always be used. If you would have made your test with a power supply your LEDs would already have died. Your luck was the inner resistance of the battery that limited the current through the LEDs.