Numbers
196, 879, 1997, 7059, 10553, 10563, 10577, 10583, 10585, 10638, 10663, 10668, 10697, 10715, 10728, 10735, 10746, 10748, 10783, 10785, 10787, 10788, 10877, 10883, 10963, 10965, 10969, 10977, 10983, 10985, 12797, 12898, 13097, 13197, 13694, 14096, 14698, 15297, 15597, 18598, 18798, 19098, 20459, 30389, 30399, 30929, 30959, 30979
Now there are many more numbers that presumably do not reach a palindrome but they join the trajectories of the above numbers at some point and thus do not fulfil the
27806, 27812, 27837, 27847, 27866, 27896, 27906, 27912, 27914, 27956, 27964, 27988, 28036, 28046, 28055, 28056, 28095, 28096, 28146, 28156, 28193, 28236, 28256, 28266, 28281, 28286, 28332, 28341, 28342, 28346, 28356, 28362, 28369, 28469, 28487, 28496, 28502, 28504, 28545, 28546, 28566, 28576, 28586, 28595, 28596, 28597, 28616, 28643, 28657, 28686, 28696, 28702, 28704, 28706, 28707, 28732, 28736, 28776, 28796, 28797, 28802, 28827, 28837, 28856, 28886, 28896, 28902, 28904, 28946, 28954, 28978, 29026, 29036, 29045, 29046, 29085, 29086, 29097, 29136, 29146, 29183, 29226, 29246, 29256, 29271, 29276, 29322, 29331, 29332, 29336, 29346, 29352, 29359, 29396, 29459, 29477, 29486, 29494, 29499, 29535, 29536, 29556, 29566, 29576, 29585, 29586, 29587, 29590, 29606, 29633, 29647, 29676, 29686, 29722, 29726, 29766, 29786, 29787, 29791, 29796, 29817, 29827, 29846, 29876, 29886, 29899, 29936, 29944, 29968, 29997, 30089, 30358, 30389, 30399, 30439, 30458, 30479, 30489, 30536, 30551, 30561, 30575, 30581, 30583, 30636, 30651, 30661, 30666, 30695, 30713, 30726, 30733, 30744, 30746, 30781, 30783, 30785, 30786, 30841, 30849, 30875, 30881, 30889, 30929, 30931, 30959, 30961, 30963, 30967, 30975, 30979, 30981, 30983, 31079, 31348, 31379, 31389, 31429, 31448, 31469, 31479, 31526, 31541, 31551, 31565, 31571, 31573, 31626, 31641, 31651, 31656, 31685, 31703, 31716, 31723, 31734, 31736, 31771, 31773, 31775, 31776, 31831, 31839, 31865, 31871, 31879, 31896, 31919, 31921, 31949, 31951, 31953, 31957, 31965, 31969, 31971, 31973, 32069, 32095, 32295, 32338, 32369, 32379, 32391, 32419, 32438, 32459, 32469, 32516, 32531, 32541, 32555, 32561, 32563, 32616, 32631, 32641, 32646, 32675, 32706, 32713, 32724, 32726, 32761, 32763, 32765, 32766, 32791, 32795, 32821, 32829, 32855, 32861, 32869, 32886, 32896, 32909, 32911, 32939, 32941, 32943, 32947, 32955, 32959, 32961, 32963, 32999, 33059, 33085, 33095, 33195, 33285, 33328, 33359, 33369, 33381, 33390, 33391, 33395, 33409, 33428, 33449, 33459, 33499, 33506, 33521, 33531, 33545, 33551, 33553, 33594, 33595, 33606, 33621, 33631, 33636, 33665, 33692, 33703, 33714, 33716, 33751, 33753, 33755, 33756, 33781, 33785, 33811, 33819, 33845, 33851, 33859, 33876, 33886, 33901, 33929, 33931, 33937, 33945, 33949, 33951, 33953, 33989, 33995, 34049, 34075, 34085, 34094, 34095, 34185, 34195, 34275, 34295, 34318, 34349, 34359, 34371, 34380, 34381, 34385, 34395, 34418, 34439, 34449, 34489, 34511, 34521, 34535, 34541, 34584, 34585, 34611, 34621, 34626, 34655, 34682, 34696, 34704, 34706, 34741, 34745, 34746, 34771, 34775, 34801, 34809, 34835, 34841, 34849, 34866, 34876, 34895, 34899, 34919, 34921, 34923, 34927, 34935, 34939, 34941, 34979, 34985, 34993, 35039, 35065, 35075, 35084, 35085, 35175, 35185, 35265, 35285, 35295, 35308, 35339, 35349, 35361, 35370, 35371, 35375, 35385, 35391, 35398, 35408, 35429, 35439, 35479, 35498, 35501, 35511, 35525, 35531, 35533, 35574, 35575, 35595, 35601, 35611, 35616, 35645, 35672, 35686, 35731, 35733, 35735, 35736, 35761, 35765, 35825, 35831, 35839, 35856, 35866, 35885, 35889, 35909, 35911, 35913, 35917, 35925, 35929, 35931, 35933, 35969, 35975, 35983, 35999, 36029, 36055, 36065, 36074, 36075, 36165, 36175, 36255, 36275, 36285, 36329, 36339, 36351, 36360, 36361, 36365, 36375, 36381, 36388, 36419, 36429, 36469, 36488, 36501, 36515, 36521, 36523, 36564, 36565, 36585, 36595, 36601, 36606, 36635, 36662, 36676, 36721, 36723, 36725, 36726, 36751, 36755, 36795, 36815, 36821, 36829, 36846, 36856, 36875, 36879, 36901, 36903, 36907, 36915, 36919, 36921, 36923, 36959, 36965, 36973, 36989, 36997, 37019, 37045, 37055, 37064, 37065, 37155, 37165, 37245, 37265, 37275, 37290, 37295, 37319, 37329, 37341, 37350, 37351, 37355, 37365, 37371, 37378, 37409, 37419, 37459, 37478, 37496, 37499, 37505, 37511, 37513, 37554, 37555, 37575, 37585, 37595, 37625, 37652, 37666, 37695, 37711, 37713, 37715, 37716, 37741, 37745, 37785, 37805, 37811, 37819, 37836, 37846, 37865, 37869, 37895, 37905, 37909, 37911, 37913, 37949, 37955, 37963, 37979, 37987, 37999, 38009, 38035, 38045, 38054, 38055, 38094, 38095, 38099, 38145, 38155, 38192, 38235, 38255, 38265, 38280, 38285, 38309, 38319, 38331, 38340, 38341, 38345, 38355, 38361, 38368, 38399, 38409, 38449, 38468, 38486, 38489, 38495, 38499, 38501, 38503, 38544, 38545, 38565, 38575, 38585, 38594, 38595, 38596, 38615, 38642, 38656, 38685, 38695, 38701, 38703, 38705, 38706, 38731, 38735, 38775, 38795, 38796, 38801, 38809, 38826, 38836, 38855, 38859, 38885, 38895, 38899, 38901, 38903, 38939, 38945, 38953, 38969, 38977, 38989, 39025, 39035, 39044, 39045, 39084, 39085, 39089, 39096, 39135, 39145, 39182, 39225, 39245, 39255, 39270, 39275, 39309, 39321, 39330, 39331, 39335, 39345, 39351, 39358, 39389, 39395, 39439, 39458, 39476, 39479, 39485, 39489, 39498, 39534, 39535, 39555, 39565, 39575, 39584, 39585, 39586, 39605, 39632, 39646, 39675, 39685, 39721, 39725, 39765, 39785, 39786, 39790, 39791, 39795, 39816, 39826, 39845, 39849, 39875, 39885, 39889, 39891, 39898, 39929, 39935, 39943, 39959, 39967, 39979, 39996
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