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interprime n.  and  Proth n.

First numbers that belong to both sets:

9, 81, 129, 225, 705, 897, 1089, 1281, 1537, 1665, 2241, 3073, 3265, 4353, 5249, 5505, 5889, 7041, 7425, 8577, 12417, 13185, 16641, 17409, 19713, 20225, 20481, 20737, 22785, 23553, 29185, 29953, 41217, 41473, 45057, 45825, 49665, 51201, 53505, 54273, 66561, 71169, 74753, 75777, 89601, 90625, 111617, 132609, 140289, 157185, 160769, 166401, 181761, 205313, 207873, 212993, 218625, 221185, 231425, 235521, 239617, 241665, 248833, 263169, 267265, 300033, 327681, 349185, 362497, 367617, 386049, 401409, 432129, 459777, 472065, 485377, 487425, 509953, 518145, 526337, 542721, 548865, 579585, 616449, 628737, 634881, 662529, 739329, 742401, 825345, 839681, 842753, 852993, 865281, 886785, 900097, 911361, 935937, 939009, 994305, 1025025, 1042433, 1089537, 1095681, 1099777, 1101825, 1157121, 1171457, 1214465, 1243137, 1261569, 1310721, 1323009, 1327105, 1396737, 1421313, 1464321, 1482753, 1495041, 1501185, 1529857, 1568769, 1581057, 1593345, 1599489, 1603585, 1611777, 1636353, 1679361, 1705985, 1787905, 1867777, 1937409, 2025473, 2078721, 2125825, 2146305, 2199553, 2201601, 2215937, 2330625, 2332673, 2404353, 2504705, 2514945, 2535425, 2580481, 2625537, 2676737, 2689025, 2717697, 2803713, 2809857, 2850817, 2883585, 2885633, 2887681, 2924545, 2985985, 3006465, 3061761, 3074049, 3153921, 3172353, 3201025, 3229697, 3239937, 3276801, 3282945, 3350529, 3405825, 3454977, 3473409, 3516417, 3551233, 3565569, 3756033, 3762177, 3770369, 3780609, 3799041, 3835905, 3866625, 3952641, 4020225, 4034561, 4038657, 4081665, 4106241, 4112385, 4143105, 4186113, 4272129, 4509697, 4530177, 4534273, 4628481, 4640769, 4702209, 4755457, 4775937, 4796417, 4853761, 4947969, 5021697, 5070849, 5083137, 5107713, 5165057, 5177345, 5357569, 5562369, 5771265, 5857281, 5922817, 5980161, 6365185, 6397953, 6475777, 6565889, 6582273, 6610945, 6660097, 6692865, 6705153, 6815745, 6852609, 6975489, 7000065, 7106561, 7135233, 7270401, 7278593, 7311361, 7503873, 7512065, 7725057, 7835649, 8081409, 8204289, 8249345, 8364033, 8699905, 8708097, 8781825, 8794113, 8896513, 9064449, 9068545, 9113601, 9121793, 9125889, 9158657, 9322497, 9359361, 9420801, 9650177, 9756673, 9785345, 9945089, 10055681, 10141697, 10194945, 10293249, 10317825, 10555393, 10600449, 10649601, 10719233, 10788865, 10895361, 10899457, 10932225, 10969089, 11005953, 11100161, 11108353, 11350017, 11403265, 11485185.

Some larger examples :