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evil n.  and  self-describing n.

First numbers that belong to both sets:

4444, 666666, 10123133, 10143331, 10153133, 10163133, 10163331, 10173133, 10173331, 10183133, 10183331, 10213223, 10232132, 10233221, 10311433, 10311633, 10311733, 10311833, 10313312, 10313315, 10313317, 10313318, 10322321, 10331231, 10331631, 10331931, 10333112, 10333115, 10333117, 10333118, 12143133, 12173133, 12173331, 12183331, 12193331, 12311533, 12311633, 12311733, 12311933, 12313310, 12313314, 12313316, 12313319, 12331631, 12331831, 12331931, 12333115, 12333117, 12333118, 14103133, 14173133, 14173331, 14183133, 14193331, 14212332, 14213223, 14232132, 14233221, 14311533, 14311733, 14311833, 14313312, 14313315, 14313317, 14313318, 14331031, 14331231, 14331531, 14331931, 14333110, 14333116, 14333119, 15103133, 15103331, 15123133, 15123331, 15143331, 15163133, 15163331, 15173133, 15173331, 15183331, 15193133, 15193331, 15212332, 15232132, 15311033, 15311233, 15311733, 15311833, 15313310, 15313314, 15313316, 15313319, 15322123, 15331231, 15331431, 15331731, 15333112, 15333117, 15333118, 16103331, 16123133, 16123331, 16143133, 16183133, 16212332, 16213223, 16233221, 16311433, 16311933, 16313312, 16313315, 16313317, 16313318, 16322321, 16331231, 16331431, 16331831, 16331931, 16333110, 16333114, 16333119, 17103133, 17123133, 17143133, 17143331, 17163133, 17163331, 17183331, 17193331, 17213223, 17233221, 17311233, 17311533, 17311833, 17311933, 17313310, 17313314, 17313316, 17313319, 17322123, 17322321, 17331031, 17331431, 17333112, 17333115, 17333118, 18103331, 18123133, 18143133, 18153331, 18163331, 18173133, 18173331, 18193133, 18193331, 18212332, 18213223, 18232132, 18233221, 18311233, 18311533, 18311933, 18313312, 18313315, 18313317, 18322321, 18331231, 18331631, 18331931, 18333110, 18333114, 18333116, 18333119, 19103331, 19143133, 19143331, 19153133, 19153331, 19163331, 19183133, 19311233, 19311433, 19311533, 19311633, 19313312, 19313315, 19313317, 19313318, 19322123, 19331731, 19333110, 19333114, 19333116, 20203332, 20323320, 20332032, 20333220, 20422420, 21102332, 21103223, 21142332, 21143223, 21153223, 21162332, 21163223, 21182332, 21192332, 21193223, 21212442, 21213233, 21213332, 21231032, 21231632, 21231932, 21233214, 21233216, 21233219, 21321023, 21321423, 21321623, 21321723, 21322133, 21322315, 21322317, 21322318, 21332132, 21422124, 21422421, 23103221, 23152132, 23153221, 23163221, 23183221, 23192132, 23193221, 23211532, 23211732, 23211832, 23213214, 23213217, 23213218, 23232442, 23234224, 23242342, 23244223, 23321021, 23321821, 23322110, 23322114, 23322116, 23322119, 24204220, 24212142, 24232342, 24243233, 24243332, 24252542, 24264226, 24284228, 24292942, 24294229, 24322433, 24323324, 24332432, 24422121, 24422525, 24422626, 25242542, 25244225, 25252442, 25332532, 25333225, 25422524, 26263233, 26263332, 26264224, 26322633, 26323326.

Some larger examples :