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inconsummate n.  and  Proth n.

First numbers that belong to both sets:

65, 161, 993, 1601, 2049, 2177, 2753, 3137, 3329, 3713, 4097, 4353, 4737, 4865, 6657, 7041, 7553, 8705, 10881, 11649, 11777, 13697, 14337, 14849, 15489, 16001, 16257, 17153, 17921, 18177, 18945, 20481, 22017, 25857, 26625, 30977, 32513, 33281, 33537, 33793, 35841, 36609, 37121, 39937, 40449, 42753, 48129, 48641, 48897, 50177, 54017, 54785, 56577, 58881, 59137, 59393, 59649, 61185, 64257, 64769, 65537, 68097, 71681, 73217, 74753, 87041, 88065, 91137, 92673, 93185, 93697, 96257, 97281, 97793, 98817, 103425, 103937, 104961, 107009, 108033, 109057, 112641, 113153, 114177, 120321, 126977, 131585, 141825, 142337, 148481, 153089, 154625, 155649, 163329, 167937, 169985, 179201, 183297, 183809, 184833, 199169, 203265, 206337, 208385, 210945, 211457, 214017, 214529, 215553, 218625, 219137, 220161, 225281, 231425, 232961, 235521, 236033, 238593, 241665, 244737, 246273, 247809, 248321, 249857, 250881, 251393, 252417, 252929, 253953, 254465, 257025, 257537, 262145, 266241, 270337, 271361, 274433, 280577, 283649, 286721, 287745, 290817, 292865, 295937, 301057, 303105, 309249, 312321, 314369, 318465, 321537, 323585, 329729, 335873, 336897, 342017, 344065, 349185, 352257, 358401, 361473, 364545, 367617, 369665, 370689, 372737, 385025, 386049, 398337, 403457, 404481, 406529, 410625, 421889, 424961, 429057, 447489, 449537, 456705, 461825, 475137, 481281, 483329, 492545, 495617, 505857, 518145, 520193, 527361, 538625, 541697, 542721, 550913, 551937, 558081, 570369, 584705, 590849, 591873, 593921, 598017, 603137, 606209, 609281, 613377, 615425, 622593, 625665, 627713, 628737, 631809, 641025, 649217, 655361, 662529, 669697, 676865, 686081, 693249, 695297, 698369, 707585, 711681, 714753, 717825, 722945, 726017, 732161, 735233, 738305, 751617, 753665, 756737, 757761, 766977, 772097, 779265, 802817, 806913, 824321, 833537, 836609, 840705, 845825, 867329, 871425, 873473, 876545, 886785, 894977, 902145, 907265, 910337, 911361, 914433, 917505, 920577, 922625, 923649, 944129, 956417, 957441, 960513, 969729, 972801, 975873, 977921, 982017, 984065, 985089, 988161, 991233, 994305.