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D-number  and  Proth n.

First numbers that belong to both sets:

9, 33, 57, 129, 177, 321, 417, 993, 1473, 1857, 2049, 2433, 3777, 4353, 4737, 7041, 8193, 10113, 10497, 12417, 13569, 13953, 16257, 19713, 20481, 25089, 28929, 32001, 36609, 42753, 47361, 50433, 52737, 56577, 63489, 64257, 68097, 77313, 86529, 89601, 98817, 108033, 109569, 112641, 123393, 128001, 131073, 132609, 144897, 160257, 163329, 174081, 177153, 183297, 190977, 192513, 197121, 214017, 220161, 223233, 224769, 238593, 261633, 266241, 306177, 312321, 324609, 330753, 386049, 389121, 407553, 416769, 444417, 459777, 478209, 499713, 524289, 536577, 542721, 545793, 551937, 601089, 616449, 628737, 637953, 647169, 653313, 690177, 736257, 766977, 773121, 819201, 831489, 837633, 865281, 896001, 929793, 939009, 957441, 969729, 988161, 1003521, 1052673, 1058817, 1089537, 1126401, 1150977, 1206273, 1366017, 1390593, 1402881, 1445889, 1482753, 1538049, 1574913, 1642497, 1648641, 1660929, 1667073, 1703937, 1851393, 1863681, 1906689, 1937409, 1943553, 2011137, 2029569, 2201601, 2220033, 2256897, 2287617, 2293761, 2342913, 2349057, 2385921, 2435073, 2508801, 2582529, 2674689, 2693121, 2766849, 2785281, 2809857, 2828289, 2840577, 2846721, 2865153, 2895873, 2988033, 3196929, 3215361, 3246081, 3289089, 3338241, 3362817, 3399681, 3454977, 3491841, 3504129, 3584001, 3602433, 3633153, 3688449, 3725313, 3731457, 3762177, 3768321, 3872769, 3878913, 3934209, 3971073, 4075521, 4118529, 4130817, 4247553, 4259841, 4333569, 4431873, 4444161, 4591617, 4616193, 4653057, 4923393, 5144577, 5206017, 5390337, 5476353, 5513217, 5537793, 5611521, 5623809, 5660673, 5685249, 5722113, 5734401, 5943297, 6029313, 6053889, 6090753, 6238209, 6422529, 6643713, 6680577, 6717441, 6840321, 6987777.