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Duffinian n.  and  Hogben n.

First numbers that belong to both sets:

21, 57, 111, 133, 183, 343, 381, 553, 651, 813, 871, 993, 1057, 1191, 1261, 1333, 1407, 1641, 1807, 1893, 1981, 2071, 2163, 2257, 2451, 2653, 2757, 2863, 3081, 3193, 3423, 3661, 3783, 4033, 4161, 4291, 4693, 4971, 5257, 5403, 5853, 6807, 6973, 7141, 7311, 7483, 7657, 7833, 8373, 8557, 8743, 8931, 9121, 9313, 9507, 9703, 10507, 10713, 10921, 11343, 11773, 11991, 12657, 12883, 13111, 13341, 13573, 14043, 15007, 15253, 15501, 15751, 16003, 16257, 16513, 16771, 17557, 17823, 18091, 18361, 18633, 19461, 19741, 20307, 20881, 21171, 21463, 22053, 22351, 22953, 23257, 23871, 24807, 25761, 26733, 27723, 28731, 29071, 29413, 30451, 30801, 31863, 32221, 32581, 32943, 33307, 33673, 34041, 34411, 35157, 36291, 36673, 37443, 38221, 38613, 39007, 39801, 40201, 40603, 41007, 41821, 42231, 43057, 43473, 44311, 44733, 45157, 45583, 46873, 47307, 48181, 48621, 49063, 49507, 49953, 50401, 50851, 51757, 52213, 52671, 53131, 54057, 54523, 54991, 56407, 56883, 57361, 57841, 58323, 58807, 59293, 59781, 61257, 61753, 62251, 62751, 63253, 63757, 64263, 64771, 65281, 66307, 66823, 67341, 67861, 68383, 68907, 69961, 70491, 71557, 72093, 72631, 73171, 73713, 74803, 75351, 75901, 76453, 77007, 78681, 79243, 80373, 80941, 81511, 82083, 84973, 86731, 87321, 87913, 88507, 89103, 89701, 90301, 90903, 91507, 92721, 93331, 93943, 94557, 95173, 97033, 97657, 99541, 100173, 100807, 101443, 102081, 102721, 103363, 104007, 105951, 107257, 107913, 109231, 109893, 112561, 113907, 114583, 115261, 115941, 116623, 117993, 119371, 120063, 122151, 122851, 124963, 126381, 127093, 128523, 129241, 129961, 130683, 131407, 132133, 132861, 133591, 135057, 137271, 138013, 138757, 140251, 141001, 141753, 142507, 144021, 146307, 147841, 148611, 150157, 150933, 151711, 152491, 153273, 154843, 155631, 157213, 158007, 159601, 160401, 162813, 165243, 166057, 167691, 169333, 170157, 170983, 172641, 174307, 175143, 175981, 176821, 177663, 178507, 179353, 181051, 182757, 183613, 184471, 185331.

Some larger examples :