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self n.  and  Sophie Germain prime

First numbers that belong to both sets:

3, 5, 53, 233, 659, 1223, 1289, 1559, 2459, 2549, 2819, 3023, 3359, 3449, 3539, 4349, 6329, 7901, 9029, 9791, 10313, 11369, 11549, 13619, 14159, 14249, 16001, 16811, 17981, 20369, 21089, 21179, 22079, 22259, 22349, 23339, 24239, 25229, 26891, 28961, 30269, 30449, 32159, 34319, 36791, 37871, 38501, 38861, 42821, 43721, 44129, 45119, 45971, 46691, 47501, 48221, 48761, 49481, 56681, 56951, 58211, 60149, 61991, 62981, 67121, 68111, 70901, 73421, 74771, 75941, 77471, 79181, 80039, 81611, 81701, 82601, 84401, 84761, 85121, 85931, 86111, 86291, 90971, 91691, 92681, 92861, 92951, 93581, 93941, 95561, 96461, 96731, 99023, 99251, 100043, 100559, 102023, 102359, 103349, 103619, 110459, 112349, 115001, 117119, 119771, 120539, 121259, 123059, 123419, 127691, 128321, 128951, 129221, 129401, 129491, 129581, 130439, 132329, 134219, 135029, 135119, 137771, 138311, 138581, 139571, 140069, 140249, 147401, 149111, 151901, 152219, 156671, 156941, 157211, 158201, 161039, 162119, 162971, 163601, 165311, 165941, 168281, 170711, 170801, 171029, 172421, 173501, 174221, 175211, 175391, 175481, 176201, 179351, 183581, 184571, 185651, 185831, 189251, 191861, 193751, 193841, 196181, 196271, 196541, 197261, 199151, 200639, 203249, 203429, 203921, 204329, 205721, 208511, 215801, 217781, 218681, 219311, 219491, 219941, 220169, 221069, 221159, 224891, 225119, 226511, 227501, 228311, 231821, 234029, 234791, 239201, 241049, 242129, 245321, 245501, 247391, 248291, 252881, 253871, 255851, 259271, 261881, 265571, 267551, 272771, 274121, 274661, 274751, 274931, 275741, 279431, 282671, 283571, 284831, 287933, 288833, 289241, 291491, 292301, 293201, 293651, 295271, 297023, 298013, 300719, 302429, 304049, 304901, 305219, 307871, 308681, 316691, 316961, 317321, 318581, 319211, 322901, 324119, 326681, 326951, 327311, 327401, 327941, 328931, 329201, 329471, 330149, 330329, 331319, 334511, 335411, 336221, 336491, 337301, 340811, 341219, 346751, 350039, 350891, 350981, 351971, 354401, 355571, 356831, 357281, 359171, 360611, 361961, 363491, 364571, 364751, 365471, 366461, 367541, 373661, 375101, 377171, 380591, 381761, 382391.

Some larger examples :