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Lehmer n.  and  Ulam n.

First numbers that belong to both sets:

451, 949, 1387, 3031, 6735, 7471, 7735, 9919, 14491, 14989, 16531, 18151, 20419, 21037, 22359, 23959, 24643, 27331, 41041, 42217, 49141, 49987, 74011, 76921, 77871, 81651, 83293, 83665, 85695, 87061, 90751, 90973, 93991, 94831, 101101, 101311, 104923, 106951, 122479, 128143, 132595, 136741, 137149, 148831, 150691, 153349, 167761, 168103, 194047, 204051, 208999, 226081, 243991, 272611, 273481, 282133, 289693, 291919, 293845, 294409, 298627, 311389, 314587, 320503, 326311, 330379, 333697, 333915, 340033, 343315, 344869, 350227, 364531, 375871, 391201, 397195, 414421, 422521, 424579, 425881, 430111, 440263, 468541, 470137, 475471, 477919, 490141, 513085, 520171, 538135, 554863, 558961, 565531, 586249, 597721, 601885, 610051, 618085, 642001, 644161, 656041, 682201, 682357, 699295, 718537, 722591, 724951, 730891, 736291, 747973, 800605, 821059, 821401, 834361, 849745, 864535, 868105, 892039, 894631, 906907, 948157, 974011, 974341, 977281, 979783, 994153, 997393, 1031953, 1037761, 1046281, 1049641, 1058281, 1064983, 1069411, 1092631, 1104271, 1107211, 1116151, 1129981, 1140547, 1268551, 1302031, 1329601, 1336105, 1357441, 1357681, 1372801, 1385245, 1400971, 1446661, 1457911, 1461241, 1467313, 1476097, 1496881, 1500661, 1531615, 1533601, 1554991, 1561921, 1564171, 1620385, 1635517, 1645391, 1671013, 1677403, 1703611, 1711711, 1727545, 1773535, 1776211, 1786969, 1806043, 1807321, 1807951, 1820845, 1833979, 1855381, 1893943, 1910791, 1911397, 1945111, 1948051, 1979701, 1994689, 2003527, 2016379, 2034871, 2067403, 2081551, 2128731, 2150617, 2183701, 2184571, 2189971, 2190511, 2195371, 2207659, 2221765, 2272381, 2299081, 2306941, 2344057, 2359243, 2386351, 2387863, 2439271, 2463385, 2493085, 2628073, 2659261, 2660881, 2684671, 2686765, 2733967, 2747785, 2780341, 2827451, 2873791, 2899801, 2921941, 2939053, 2940211, 3012241, 3072049, 3075521, 3094771, 3103741, 3120307, 3178627, 3192711, 3198805, 3199201, 3215941, 3252991, 3306493, 3370921, 3404047, 3423421, 3452281, 3459061, 3470641, 3479887, 3504187, 3557569, 3593551, 3597595, 3649051, 3658901, 3660631, 3713311, 3723811, 3747901, 3748345, 3770515, 3784249, 3788335, 3803479, 3833011, 3845167, 3882151, 3902671, 3909781, 3931291, 3940867, 3955381, 3977611, 3985921, 4063501, 4070389, 4088773, 4103683, 4177507, 4234021, 4240171, 4252381, 4261153, 4262881, 4284781, 4324741.

Some larger examples :