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cyclic n.  and  Ruth-Aaron pair

First numbers that belong to both sets:

5, 15, 77, 493, 949, 2491, 5561, 5959, 6557, 12351, 14587, 16933, 17081, 20451, 24433, 24881, 24895, 26643, 33019, 37829, 40081, 44831, 47545, 48203, 49241, 52555, 63427, 63665, 98119, 99163, 106799, 109939, 132209, 143623, 154843, 155111, 173163, 197657, 204259, 224257, 261019, 263629, 268657, 296111, 319429, 329989, 332995, 346693, 350599, 361063, 370349, 373703, 380963, 384313, 394855, 417163, 441211, 467303, 509851, 537917, 540281, 554683, 565823, 583463, 598249, 608317, 618751, 624079, 639847, 685229, 693611, 732089, 732199, 748231, 773313, 788671, 820601, 839199, 856607, 859409, 878899, 890723, 906019, 911537, 917863, 961573, 962141, 977281, 977779, 1006549, 1023641, 1045951, 1053599, 1054829, 1104263, 1131811, 1172947, 1173149, 1191133, 1191451, 1199987, 1232747, 1243501, 1246933, 1252509, 1263679, 1267919, 1275731, 1293139, 1306247, 1428857, 1492031, 1496551, 1516787, 1549455, 1560499, 1562093, 1570279, 1600963, 1618789, 1672711, 1716629, 1744919, 1797113, 1799941, 1806367, 1806949, 1818227, 1838183, 1858645, 1864057, 1915577, 1945049, 1962797, 2009351, 2020801, 2022343, 2029949, 2042951, 2049319, 2065123, 2101285, 2120989, 2128985, 2138171, 2138929, 2179519, 2238373, 2260589, 2305397, 2339047, 2442185, 2493799, 2527019, 2538533, 2579309, 2586235, 2701657, 2742395, 2834767, 2854739, 2892103, 2932345, 2975951, 3003469, 3009413, 3013915, 3026019, 3161665, 3223789, 3265805, 3394015, 3402311, 3423437, 3438521, 3457497, 3468319, 3476965, 3524497, 3561941, 3570731, 3573467, 3584053, 3584195, 3602833, 3668587, 3678809, 3696379, 3703589, 3743351, 3749429, 3772333, 3790955, 3844279, 3889343, 3897529, 3912337, 3950119, 3975059, 4057123, 4086227, 4124537, 4150805, 4187293, 4187659, 4281467, 4285957, 4339369, 4382689, 4389539, 4389569, 4462339, 4494749, 4596863, 4647221, 4763627, 4832665, 4846993, 4854877, 4868781, 4913219, 4913981, 4929799, 4958989, 5034551, 5142955, 5152757, 5185519, 5195089, 5241035, 5242031, 5362347, 5378757, 5384399, 5408461, 5432719, 5535655, 5615051, 5686307, 5733847, 5739449, 5801081, 5854085, 5898299, 5928251, 5932873, 5945777, 5963549, 6024269, 6029173, 6059083, 6126439, 6161833, 6226399, 6242131, 6287867, 6296777, 6476147, 6486299, 6491059, 6587089, 6597155, 6649049, 6668947, 6829073, 6890179, 6897593, 6905999, 6963437, 6981341, 7036871, 7073113, 7084297, 7094933, 7142969, 7160245, 7185385, 7191735, 7304433, 7322143.

Some larger examples :