Transformer draining voltage from arduino trhough LM317t

This is sounding strange...

Maybe high-frequency noise / coupling?? Make sure you have a bypass capacitor (say .1uf) right across the 74141 Vcc-Gnd supply. Make sure you have a similar value (but you may need a 200v or more rating) across the DC output of your Nixie power supply...

Something invisible other-than-DC seems to be happening here. Maybe.