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happy n.  and  Honaker prime

First numbers that belong to both sets:

263, 1039, 1933, 2221, 3067, 3137, 5741, 6343, 6353, 6971, 7481, 8821, 9103, 10247, 11251, 12347, 13037, 13339, 13457, 13933, 14437, 16451, 17317, 18041, 21617, 26309, 26339, 30091, 30293, 31177, 32009, 34471, 35227, 36307, 36433, 37117, 41131, 41333, 41801, 43781, 50417, 51473, 52543, 54941, 55207, 57089, 57713, 58321, 62627, 63607, 64151, 66301, 68903, 70039, 70379, 71261, 72701, 73009, 74231, 76159, 78283, 79273, 82051, 84017, 86243, 95111, 95219, 96553, 103969, 111443, 113357, 120473, 120511, 123217, 129113, 131371, 132283, 132721, 135731, 136217, 137437, 139409, 141301, 143357, 144307, 149113, 151337, 152123, 154073, 156253, 157307, 160603, 162553, 163117, 163127, 163363, 164621, 165211, 172807, 173297, 175433, 180241, 182233, 185149, 185491, 186229, 186727, 187027, 191341, 192461, 196307, 196429, 197273, 203227, 203417, 209159, 211469, 213721, 215161, 215563, 215981, 216523, 217517, 218419, 218629, 219533, 230309, 232207, 237179, 240173, 245209, 256801, 260363, 260581, 261071, 265123, 265231, 265241, 267017, 269221, 270167, 272203, 275711, 278233, 280351, 280513, 281233, 282307, 283501, 285473, 285631, 286771, 297247, 297371, 300137, 303931, 305771, 306503, 307169, 308293, 313373, 314357, 314641, 317831, 325723, 325861, 328093, 330359, 331871, 332069, 332399, 333383, 333493, 334771, 336793, 338171, 340633, 340643, 340919, 341057, 343771, 344543, 346349, 347747, 353711, 356333, 362851, 366001, 370103, 371057, 374317, 374501, 375113, 375341, 389047, 392111, 392221, 400871, 402823, 404419, 405553, 405611, 405731, 407401, 407801, 408223, 408263, 410119, 410617, 411193, 418031, 419351, 421661, 422797, 423587, 425443, 427433, 431191, 432743, 434561, 434611, 435191, 435731, 438701, 440159, 441113, 441461, 444109, 445091, 449851, 450949, 452923, 462641, 471061, 473173, 473477, 474307, 476591, 479309, 491581, 501967, 502429, 502507, 504877, 515153, 522037, 525353, 526051, 526423, 526531, 531551, 537041, 550027, 550609, 552751, 553153, 555073, 555307, 556841, 562021, 562201, 569711, 572711, 573107, 574031, 580717, 581921, 583153, 591431, 594617, 596741, 600307, 600893, 601451, 602039, 609199, 609617, 609751, 612511, 619813.

Some larger examples :