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happy n.  and  modest n.

First numbers that belong to both sets:

13, 19, 23, 49, 79, 103, 109, 133, 203, 409, 622, 709, 763, 818, 833, 836, 888, 899, 1003, 1009, 1030, 1033, 1090, 1218, 1222, 1233, 1299, 1333, 1339, 1418, 1527, 1533, 1599, 1636, 1666, 1733, 1881, 1933, 2003, 2030, 2036, 2111, 2133, 2177, 2199, 2333, 2369, 2545, 2555, 2575, 2639, 2833, 2844, 2899, 2933, 3133, 3193, 3233, 3296, 3466, 3563, 3654, 4009, 4090, 4111, 4148, 4222, 4555, 4599, 4872, 4888, 5066, 5111, 5199, 5499, 5555, 5666, 5799, 6037, 6293, 6899, 7009, 7063, 7090, 7599, 8018, 8036, 8074, 8088, 8099, 8108, 8299, 8333, 8699, 9037, 10003, 10009, 10030, 10033, 10090, 10185, 10222, 10303, 10333, 10666, 12018, 12074, 12081, 12108, 12148, 12333, 13037, 13039, 13111, 13481, 14018, 14027, 14074, 14333, 14378, 15027, 15081, 16036, 16144, 16222, 16999, 17027, 17999, 18074, 18081, 18111, 18243, 19171, 19333, 20003, 20030, 20036, 20111, 20185, 20333, 20555, 21081, 21333, 22054, 22594, 23069, 23851, 24111, 24222, 24324, 24444, 24999, 25027, 25045, 25075, 25111, 25675, 25925, 26039, 26117, 27243, 28054, 28074, 28108, 28126, 28378, 28666, 30135, 31037, 31093, 31111, 32096, 32148, 32864, 34111, 34306, 34666, 35063, 35555, 36037, 36054, 36162, 37999, 38114, 38333, 40009, 40090, 40111, 40148, 40222, 40555, 40888, 41123, 41333, 42111, 42222, 42259, 42567, 42777, 42999, 43111, 44074, 44108, 44222, 44407, 45111, 45243, 45333, 45405, 46333, 47111, 47423, 48072, 48324, 48432, 48592, 48666, 49111, 49441, 50111, 50555, 50666, 51081, 52054, 52074, 52108, 52111, 52156, 52702, 54111, 54162, 54243, 54333, 55999, 56252, 56444, 56777, 57081, 57513, 58261, 59111, 59333, 60022, 60202, 60370, 61999, 62093, 63777, 64148, 64333, 64444, 67603, 68111, 68666, 70009, 70063, 70090, 70185, 70518, 70630, 71639, 71999, 72162, 72216, 72243, 72324, 73999, 74111, 75081, 75135, 76114, 76222, 76363, 76444, 76666, 77259, 78999, 79111, 79237, 80018.

Some larger examples :