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alternating n.  and  happy n.

First numbers that belong to both sets:

1, 7, 10, 23, 32, 49, 70, 94, 103, 109, 129, 167, 230, 236, 301, 329, 365, 367, 383, 478, 490, 496, 563, 565, 632, 638, 656, 694, 709, 761, 763, 818, 836, 874, 901, 907, 921, 923, 989, 1030, 1076, 1090, 1092, 1212, 1218, 1258, 1274, 1290, 1418, 1472, 1474, 1478, 1636, 1670, 1812, 1814, 1818, 1852, 1874, 2109, 2121, 2147, 2181, 2185, 2309, 2369, 2383, 2527, 2545, 2547, 2581, 2725, 2741, 2745, 2901, 2903, 2963, 2989, 3010, 3038, 3056, 3076, 3092, 3238, 3290, 3296, 3436, 3456, 3616, 3634, 3650, 3654, 3670, 3676, 3692, 3698, 3830, 3832, 3896, 4127, 4147, 4181, 4187, 4363, 4365, 4525, 4527, 4545, 4563, 4585, 4721, 4725, 4741, 4747, 4781, 5036, 5056, 5218, 5254, 5272, 5274, 5436, 5452, 5454, 5458, 5472, 5630, 5634, 5650, 5812, 5854, 6107, 6163, 6305, 6307, 6329, 6343, 6345, 6361, 6367, 6389, 6503, 6505, 6543, 6701, 6703, 6763, 6789, 6923, 6983, 6987, 6989, 7016, 7036, 7090, 7214, 7252, 7254, 7412, 7414, 7418, 7452, 7474, 7610, 7630, 7636, 7698, 7814, 7878, 7896, 8121, 8125, 8141, 8147, 8181, 8303, 8323, 8369, 8521, 8545, 8741, 8769, 8787, 8909, 8929, 8963, 8967, 8969, 9010, 9012, 9032, 9070, 9098, 9210, 9230, 9236, 9298, 9632, 9638, 9678, 9698, 9836, 9876, 9890, 9892, 9896, 10121, 10125, 10141, 10185, 10303, 10309, 10323, 10521, 10527, 10547, 10581, 10587, 10725, 10727, 10745, 10769, 10785, 10903, 10929, 10967, 12101, 12105, 12123, 12129, 12141, 12143, 12149, 12167, 12183, 12303, 12321, 12341, 12347, 12381, 12385, 12501, 12507, 12565, 12583, 12705, 12707, 12729, 12743, 12761, 12767, 12787, 12909, 12921, 12927, 12941, 12969, 14101, 14121, 14123, 14129, 14165, 14167, 14183, 14321, 14327, 14347, 14381, 14387, 14507, 14549, 14561, 14565, 14705, 14723, 14743, 14761, 14783, 14921, 14945.

Some larger examples :