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aban n.  and  Proth n.

First numbers that belong to both sets:

3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, 257, 289, 321, 353, 385, 417, 449, 481, 513, 545, 577, 609, 641, 673, 705, 737, 769, 801, 833, 865, 897, 929, 961, 993, 1000449, 2000897, 3000321, 6000641, 7000065, 13000705, 14000129, 27000833, 28000257, 41000961, 42000385, 56000513, 84000769, 85000193, 113000449, 141000705, 142000129, 169000961, 170000385, 198000641, 199000065, 226000897, 227000321, 255000577, 256000001, 284000257, 340000769, 369000449, 398000129, 425000961, 454000641, 483000321, 512000001, 539000833, 568000513, 597000193, 653000705, 682000385, 711000065, 738000897, 767000577, 796000257, 852000769, 881000449, 910000129, 937000961, 966000641, 995000321, 1024000001, 1051000833, 1109000193, 1194000385, 1279000577, 1364000769, 1422000129, 1449000961, 1507000321, 1592000513, 1677000705, 1735000065, 1762000897, 1820000257, 1905000449, 1990000641, 2048000001, 2075000833, 2133000193, 2218000385, 2303000577, 2388000769, 2446000129, 2473000961, 2531000321, 2616000513, 2701000705, 2759000065, 2786000897, 2844000257, 2929000449, 3014000641, 3072000001, 3099000833, 3157000193, 3242000385, 3327000577, 3412000769, 3470000129, 3497000961, 3555000321, 3640000513, 3725000705, 3783000065, 3810000897, 3868000257, 3953000449, 4038000641, 4096000001, 4123000833, 4181000193, 4266000385, 4436000769, 4579000321, 4749000705, 4892000257, 5062000641, 5205000193, 5375000577, 5518000129, 5545000961, 5688000513, 5831000065, 5858000897, 6001000449, 6144000001, 6171000833, 6314000385, 6484000769, 6627000321, 6797000705, 6940000257, 7110000641, 7253000193, 7423000577, 7566000129, 7593000961, 7736000513, 7879000065, 7906000897, 8049000449, 8192000001, 8219000833, 8362000385, 8532000769, 8675000321, 8845000705, 8988000257, 9158000641, 9301000193, 9471000577, 9614000129, 9641000961, 9784000513, 9927000065, 9954000897, 10097000449, 10240000001, 10267000833, 10410000385, 10580000769, 10723000321, 10893000705, 11036000257, 11206000641, 11349000193, 11519000577, 11662000129, 11689000961, 11832000513, 11975000065, 12002000897, 12145000449, 12288000001, 12315000833, 12458000385, 12628000769, 12771000321, 12941000705, 13084000257, 13254000641, 13397000193, 13567000577, 13710000129, 13737000961, 13880000513, 14023000065, 14050000897, 14193000449, 14336000001, 14363000833, 14506000385, 14676000769, 14819000321, 14989000705, 15132000257, 15302000641, 15445000193, 15615000577, 15758000129, 15785000961, 15928000513, 16071000065, 16098000897, 16241000449, 16384000001, 16411000833, 16554000385, 16724000769, 16867000321, 17037000705, 17350000641, 17663000577, 17976000513, 18289000449, 18602000385, 18915000321, 19228000257, 19541000193, 19854000129, 19881000961, 20167000065, 20194000897, 20480000001, 20507000833, 20820000769, 21133000705, 21446000641, 21759000577, 22072000513, 22385000449, 22698000385, 23011000321, 23324000257, 23637000193, 23950000129, 23977000961, 24263000065, 24290000897, 24576000001, 24603000833, 24916000769, 25229000705, 25542000641, 25855000577, 26168000513.

Some larger examples :