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junction n.  and  self-describing n.

First numbers that belong to both sets:

444422, 10173331, 10193331, 10213223, 10233221, 10313315, 10313317, 10313319, 10322123, 10322321, 10331731, 10331931, 10333115, 10333117, 10333119, 12153331, 12173331, 12193133, 12193331, 12311033, 12311933, 12313315, 12313317, 12313319, 12331031, 12331531, 12331731, 12331931, 12333115, 12333117, 12333119, 14153331, 14173133, 14173331, 14193133, 14193331, 14213223, 14233221, 14311033, 14311733, 14311933, 14313315, 14313317, 14313319, 14322123, 14322321, 14331031, 14331531, 14331731, 14331931, 14333115, 14333117, 14333119, 15123331, 15143331, 15163133, 15163331, 15183133, 15183331, 15311633, 15311833, 15313316, 15313318, 15331231, 15331431, 15331631, 15331831, 15333116, 15333118, 16153133, 16153331, 16173133, 16173331, 16193133, 16193331, 16213223, 16233221, 16311033, 16311533, 16311733, 16311933, 16313317, 16313319, 16322123, 16322321, 16331031, 16331531, 16331731, 16331931, 16333117, 16333119, 17103331, 17123331, 17143133, 17143331, 17163133, 17163331, 17183133, 17183331, 17212332, 17232132, 17311433, 17311633, 17311833, 17313318, 17331231, 17331431, 17331631, 17331831, 17333118, 18153133, 18153331, 18173133, 18173331, 18193133, 18193331, 18213223, 18233221, 18311033, 18311533, 18311733, 18311933, 18313319, 18322123, 18322321, 18331031, 18331531, 18331731, 18331931, 18333119, 19103331, 19123133, 19123331, 19143133, 19143331, 19163133, 19163331, 19183133, 19183331, 19212332, 19232132, 19311233, 19311433, 19311633, 19311833, 19331031, 19331231, 19331431, 19331631, 19331831, 20204224, 20244220, 20422024, 20422420, 21103223, 21143223, 21163223, 21172332, 21183223, 21192332, 21214224, 21231032, 21231732, 21231932, 21233215, 21233217, 21233219, 21244221, 21321023, 21321423, 21321623, 21321823, 21322315, 21322317, 21322319, 21422124, 21422421, 23103221, 23143221, 23163221, 23172132, 23183221, 23192132, 23211032, 23211732, 23211932, 23213215, 23213217, 23213219, 23234224, 23244223, 23321021, 23321421, 23321621, 23321821, 23322115, 23322117, 23322119, 23422324, 23422423, 24204220, 24214221, 24234223, 24243233, 24243332, 24254225, 24264226, 24274227, 24282842, 24284228, 24292942, 24294229, 24322433, 24332432, 24422020, 24422121, 24422323, 24422525, 24422626, 24422727, 24422828, 24422929, 25244225, 25253233, 25253332, 25254224, 25322533, 25332532, 25422425, 25422524, 26244226, 26263233, 26263332, 26264224, 26322633, 26332632, 26422426, 26422624, 27244227, 27273233, 27273332, 27274224, 27322733, 27332732, 27422427, 27422724, 28242842, 28244228, 28282442, 28283233, 28283332, 28322833, 28332832, 28422428, 29242942, 29244229, 29292442, 29293233, 29293332, 29322933, 29332932, 29422429, 31103315, 31103317, 31103319, 31121033, 31121933, 31123315, 31123317, 31123319, 31141033, 31141733, 31141933, 31143315, 31143317, 31143319, 31151633, 31151833, 31153316, 31153318.

Some larger examples :