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self n.  and  star n.

First numbers that belong to both sets:

1, 121, 793, 2773, 3313, 4213, 6733, 14113, 17173, 19153, 24193, 26533, 28153, 30673, 41833, 52453, 70633, 81433, 103753, 115093, 123553, 141373, 150733, 170353, 213193, 281233, 313273, 321553, 327133, 388621, 400933, 410293, 426133, 439021, 468721, 559981, 571033, 620173, 754021, 779761, 846001, 868681, 877837, 938521, 957601, 981721, 986581, 1040833, 1101673, 1117153, 1180153, 1250353, 1261333, 1379521, 1402633, 1420093, 1521073, 1600633, 1613053, 1656901, 1688581, 1785421, 1798537, 1844821, 1884961, 1898437, 1945981, 1952821, 1987201, 2113453, 2199781, 2207053, 2221633, 2340001, 2377621, 2538901, 2689381, 2729701, 2737801, 2778481, 2794837, 2803033, 2935801, 2986381, 3011833, 3080233, 3193021, 3210553, 3379501, 3562021, 3599101, 3645721, 3739861, 3787381, 3844801, 3883321, 4078801, 4088701, 4289221, 4329901, 4381021, 4422133, 4546621, 4757941, 4779337, 4854601, 4865401, 4919581, 5083921, 5183821, 5194981, 5295961, 5363821, 5466421, 5639581, 5709601, 5768281, 5791837, 5874661, 5886541, 5946121, 6102433, 6248521, 6309901, 6359221, 6495841, 6545881, 6608701, 6684481, 6709837, 6927301, 7069861, 7095937, 7187581, 7266601, 7319521, 7385941, 7399261, 7492837, 7519681, 7668181, 7695337, 7790761, 7928101, 8290801, 8347321, 8560981, 8632801, 8647201, 8719381, 8748337, 8777341, 8864641, 9084781, 9158761, 9188437, 9292681, 9307621, 9382501, 9442621, 9608941, 9639337, 9746101, 9761401, 9838081, 9992341, 10069921, 10273033, 10320193, 10926901, 11040553, 11073133, 11122093, 11269621, 11667781, 11684521, 11768401, 11835721, 12089881, 12277981, 12502153, 12536821, 12693421, 12798361, 12868561, 12956581, 12974221, 13491001, 13509001, 13599181, 13871521, 13944601, 14874301, 14893201, 15273721, 15446521, 15465781, 15639661, 15736681, 15756121, 15853501, 15892537, 15931621, 16186837, 16344901, 16483837, 16743421, 16783537, 16823701, 16924321, 16944481, 17005033, 17085937, 17227981, 17248321, 17431921, 17554861, 17657641, 17843401, 17864101, 18030133, 18280621, 18364501, 18490681, 18596161, 18638437, 18680761, 18914401, 19278337, 19429201, 19450801, 19645741, 19754461, 19776241, 20170333, 20635021, 20768761, 21015073, 21240253, 21512053, 21557521, 21648601, 21762721, 21785581, 21945937, 21991861, 22129921, 22337821, 22476961, 22639837, 22686481, 22826701, 22943881, 22990837, 23014333, 23297221, 23391901, 23748661, 23868181, 23892121, 24591601, 24615901, 24737581, 24786337, 24957361, 24981841, 25325821, 25473961, 25572961, 25721821, 25846201, 26095861, 26447401, 26472601, 26649337, 26826661, 27081001, 27208621, 27464761, 27593281.

Some larger examples :