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amenable n.  and  self-describing n.

First numbers that belong to both sets:

4444, 224444, 442244, 10123133, 10143133, 10153133, 10163133, 10173133, 10183133, 10193133, 10212332, 10232132, 10233221, 10311233, 10311433, 10311533, 10311633, 10311733, 10311833, 10311933, 10313312, 10313316, 10313317, 10322321, 10333112, 10333116, 10333117, 12103133, 12143133, 12153133, 12163133, 12173133, 12183133, 12193133, 12311033, 12311433, 12311533, 12311633, 12311733, 12311833, 12311933, 12313316, 12313317, 12333116, 12333117, 14103133, 14123133, 14153133, 14163133, 14173133, 14183133, 14193133, 14212332, 14232132, 14233221, 14311033, 14311233, 14311533, 14311633, 14311733, 14311833, 14311933, 14313312, 14313316, 14313317, 14322321, 14333112, 14333116, 14333117, 15103133, 15123133, 15143133, 15163133, 15173133, 15183133, 15193133, 15212332, 15232132, 15233221, 15311033, 15311233, 15311433, 15311633, 15311733, 15311833, 15311933, 15313312, 15313316, 15313317, 15322321, 15333112, 15333116, 15333117, 16103133, 16123133, 16143133, 16153133, 16173133, 16183133, 16193133, 16212332, 16232132, 16233221, 16311033, 16311233, 16311433, 16311533, 16311733, 16311833, 16311933, 16313312, 16313317, 16322321, 16333112, 16333117, 17103133, 17123133, 17143133, 17153133, 17163133, 17183133, 17193133, 17212332, 17232132, 17233221, 17311033, 17311233, 17311433, 17311533, 17311633, 17311833, 17311933, 17313312, 17313316, 17322321, 17333112, 17333116, 18103133, 18123133, 18143133, 18153133, 18163133, 18173133, 18193133, 18212332, 18232132, 18233221, 18311033, 18311233, 18311433, 18311533, 18311633, 18311733, 18311933, 18313312, 18313316, 18313317, 18322321, 18333112, 18333116, 18333117, 19103133, 19123133, 19143133, 19153133, 19163133, 19173133, 19183133, 19212332, 19232132, 19233221, 19311033, 19311233, 19311433, 19311533, 19311633, 19311733, 19311833, 19313312, 19313316, 19313317, 19322321, 19333112, 19333116, 19333117, 20203233, 20203332, 20204224, 20244220, 20322033, 20323320, 20332032, 20333220, 20422024, 20422420, 21102332, 21142332, 21152332, 21162332, 21172332, 21182332, 21192332, 21213233, 21213332, 21214224, 21231032, 21231432, 21231532, 21231632, 21231732, 21231832, 21231932, 21233216, 21233217, 21244221, 21322133, 21322316, 21322317, 21323321, 21332132, 21333221, 21422124, 21422421, 23102132, 23103221, 23142132, 23143221, 23152132, 23153221, 23162132, 23163221, 23172132, 23173221, 23182132, 23183221, 23192132, 23193221, 23211032, 23211432, 23211532, 23211632, 23211732, 23211832, 23211932, 23213216, 23213217, 23234224, 23321021, 23321421, 23321521, 23321621, 23321721, 23321821, 23321921, 23322116, 23322117, 23422324, 24204220, 24214221, 24243233, 24243332, 24254225, 24284228, 24294229, 24322433, 24323324, 24332432, 24333224, 24422020, 24422121, 24422525, 24422828, 24422929, 25244225, 25253233, 25253332, 25254224, 25322533, 25323325, 25332532.

Some larger examples :