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Friedman n.  and  junction n.

First numbers that belong to both sets:

216, 1022, 1024, 2507, 2509, 4624, 5120, 7928, 11025, 12104, 12106, 12108, 13725, 13822, 13824, 13826, 15612, 15618, 15620, 15622, 15624, 15626, 15628, 16225, 16815, 17325, 17428, 17925, 18225, 18522, 19321, 25314, 26624, 28224, 28226, 29524, 29526, 30625, 31509, 32815, 32825, 34425, 35721, 35933, 36918, 38427, 39216, 39424, 42025, 43932, 46624, 46626, 46630, 46632, 53824, 54726, 56732, 59039, 59129, 59319, 65528, 70225, 73125, 76835, 78116, 78126, 78132, 78225, 78732, 81225, 81920, 83524, 91125, 95232, 97333, 98435, 102510, 102912, 103824, 104026, 104916, 105021, 105025, 105210, 105624, 105723, 108126, 109525, 112509, 112923, 113724, 114921, 115625, 116317, 116725, 116729, 116828, 117316, 117619, 117623, 117625, 117627, 117629, 117726, 117728, 118327, 119025, 124415, 124926, 125008, 125010, 125012, 125014, 125016, 125018, 125019, 125020, 125021, 125022, 125023, 125025, 125027, 125029, 125031, 125033, 125315, 125317, 127428, 127620, 127933, 128326, 128633, 130321, 132527, 132715, 132725, 133225, 133815, 134725, 134832, 135429, 135625, 136214, 136525, 136927, 137623, 137625, 137718, 137728, 137732, 137823, 137920, 137924, 137928, 138624, 139621, 139932, 140035, 140625, 143325, 145117, 145832, 145923, 146330, 146415, 146417, 146419, 146520, 146827, 147519, 147525, 147925, 148223, 148225, 150030, 150624, 150826, 151728, 155516, 155520, 156024, 156127, 156218, 156226, 156315, 156325, 156933, 157423, 157922, 160427, 161025, 161115, 162526, 162720, 163125, 163216, 163525, 163832, 164025, 165834, 168520, 172224, 172822, 174820, 175623, 175932, 176832, 176925, 177435, 178632, 178929, 179334, 180225, 180621, 180625, 183624, 183729, 184126, 184320, 185220, 185935, 186621, 186623, 186625, 186627, 186629, 186631, 186633, 186635, 187029, 187230, 192721, 193635, 194426, 194521, 194523, 194723, 195318, 195322, 195328, 195736, 196527, 196624, 196626, 196632, 196824, 196830, 196832, 196935, 197320, 197730, 198024, 205419, 208624, 214326, 215424, 215832, 216009, 216011, 216013, 216015, 216017, 216019, 216020, 216021, 216022, 216023, 216024, 216026, 216028, 216030, 216032, 216034, 216225, 219024, 219025, 219824, 219834, 223524, 225619.

Some larger examples :