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Harshad n.  and  self-describing n.

First numbers that belong to both sets:

10313316, 10333116, 12153331, 12173133, 12311733, 12313314, 12333114, 14212332, 14232132, 14313312, 14333112, 14333117, 15143331, 15311033, 16193331, 16313310, 16313319, 16333110, 17311033, 17311433, 17311833, 17313318, 17322123, 18173133, 18313317, 18331731, 19103133, 19163331, 19233221, 19311033, 19313316, 20204224, 20323320, 20333220, 21142332, 21212442, 21214224, 21231432, 21233214, 21242142, 21322314, 21323321, 21422124, 23142132, 23211432, 23213214, 23322110, 23322114, 23322117, 24212142, 25242542, 25323325, 25333225, 26263332, 26264224, 26323326, 27332732, 28284224, 31103316, 31123314, 31143312, 31143315, 31153312, 31153316, 31163310, 31163319, 31181733, 31193316, 31331016, 31331214, 31331412, 31331510, 31331610, 31331718, 32152123, 32203320, 32212314, 32212315, 32232114, 32253325, 32263326, 32332020, 32332525, 33103112, 33103116, 33103119, 33123114, 33143112, 33163110, 33173112, 33173118, 33181731, 33191231, 33203220, 33253225, 33311012, 33311016, 33311019, 33311214, 33311412, 33311610, 33311712, 33311817, 33311912, 33322020, 33322525, 42212124, 1017313322, 1041184144, 1041411644, 1241154144, 1241154441, 1244154141, 1310414144, 1319414144, 1341194144, 1417223331, 1417313322, 1422173133, 1422313317, 1422331731, 1431172233, 1431223317, 1431331722, 1433172231, 1433173122, 1433223116, 1510313322, 1516332231, 1516333122, 1517414144, 1522103331, 1522313310, 1522331631, 1522333116, 1531103322, 1531331622, 1531332216, 1541124144, 1541124441, 1541174144, 1541411744, 1544124141, 1615223133, 1615312233, 1618414144, 1622153331, 1622311933, 1622331531, 1631153322, 1631331522, 1631331722, 1633143122, 1633223115, 1633312215, 1641411044, 1641414413, 1641444112, 1710414144, 1710414441, 1710444141, 1714223331, 1714313322, 1715414144, 1716313322, 1718313322, 1719414144, 1722143133, 1722183331, 1722313314, 1722331431, 1731142233, 1731223314, 1731331422, 1733142231, 1733143122, 1741154144, 1741194144, 1741411944, 1741414410, 1741444110, 1744414110, 1810414144, 1831153322, 1841134144, 1841411644, 1841444113, 1844414116, 1913414144, 1917414144, 1922313314, 1933223114, 1933223116, 1941134144, 1941174144, 1941411744, 2210313315, 2210313317, 2215103331, 2215163133, 2215311633, 2215313310, 2216153331, 2216331531, 2217103331, 2217331031, 2218311733, 2219143133, 2231103315, 2231141733, 2231153316, 2231171433, 2231331516, 2233141731, 2233163114, 2233163115, 2233171431, 2233171831, 2233311017, 2233311518, 2233311615, 2626424244, 2642264244, 2642422644, 2929424442, 3110331722, 3114223319, 3115162233, 3115182233, 3115221633, 3116153322, 3116331522, 3117221833, 3122141733, 3122153316, 3122171433, 3122331516, 3122331718, 3133101722, 3133141622, 3133141722, 3133151822, 3133162214, 3133162215, 3133162219, 3133171422, 3133221416, 3133221615, 3310311522, 3310312215, 3314221731, 3314311722, 3314311922, 3315102231, 3315312210, 3316152231, 3316153122, 3316221931, 3317221431, 3317223116, 3317311022, 3317311422, 3322101531, 3322151631, 3322153116, 3322311417, 3322311510, 3322311714, 3331101522, 3331102215, 3331151622, 3331152216, 3331221417, 3331221714, 4110174144, 4110174441, 4110411744, 4110411844, 4110414417, 4110441741.

Some larger examples :