repeating number, when n is multiple of 3. If we take any integer  multiple of $3$, and add up the cubes of its decimal digits, then take 
the result and sum the cubes of its digits, and so on, we invariably end up with $153.$

Why the above result is true for only an integer multiple of $3?$ can we prove the reasons for it? Is there any such numbers will invariably end with any number and not multiple of $3?$ If yes, how to find them.
A number is only divisible by three if the sum of its digits is a multiple of three. Since $a^3\equiv a\mod 3$, we see that after applying the 'step' (the function $s$) to a number divisible by three will still be divisible by three. Also, a number not divisible by $3$ will never be divisible by three after the step (because everything here works in two directions). Since $3|153$ (because $3|1+5+3=9$), only numbers divisible by $3$ can end in $153$.

In general, because $9^3&lt;1000$, $s(n)&lt;n$ when $n&gt;10000$ and $s(n)&lt;10000$ when $n\leq 10000$ (these are not a sharp bounds). This implies that the sequence $\left(s^k(n)\right)_{k\geq 0}$ will be decreasing until it falls below $10000$. Because of that, the function will eventually get in a finite loop. Thus, there is an $l$ such that, for a sufficient large $K$, $s^{k+l}(n)=s^k(n)$ for all $k&gt;K$. It is possible to calculate all fixpoints $n$ of $s$ for which $s(n)=n$. I think this only applies to $153$, since it is given in this problem, but maybe there are some other numbers with this property.

EDIT As user44197 points out, the only other fixpoints (I assume) are $370$, $371$ and $407$. And of course $0$ and $1$, but they are trivial. As you can see, none of these numbers is divisible by $3$, so they can only end up in $153$ or in a cycle, but there aren't any cycles apparently. For other numbers then $3$, I don't know whether or not multiples will always end in the same number, but I think not. The only number that may be of interest is $11$, because a number is a multiple of $11$ when the alternating sum of its digits is a multiple of $11$. Problem is that $2^3=8\neq \pm 2\mod11$, so divisibility it not conserved. For any other interesting numbers, you can search for $n$ s.t. $i^3\equiv \pm i\mod n$ for all $1\leq i\leq n$. Thus, $2^3=8\equiv \pm 2\mod n$. This is true for $n=2$, $n=3$, $n=5$, $n=6$ and $n=10$. $n=2$ doesn't work, because $s(12)=1+8=9$ and $9$ is odd. Same for $n=10$: $s(10)=1+0=1$. For $n=6$, we get $s(12)=9$. For $n=5$, we get $s(10)=1$, so this won't work either. Thus, only multiples of $3$ have the property that they are still multiples of $3$ after applying $s$.
is not an answer but an observation which should inspire the Researchers to identify the patterns(if any)

First of all, some cycle converges to  Armstrong Numbers (a special case of Narcissistic number).

Rest form very small cycles 

$$1=[1, 10, 100, 112, 121, 211, 778, 787, 877, 1000, 1012, 1021, 1102, 1120, 1189, 1198, 1201, 1210, 1234, 1243, 1324, 1342, 1423, 1432, 1579, 1597, 1759, 1795, 1819, 1891, 1918, 1957, 1975, 1981, 2011, 2101, 2110, 2134, 2143, 2314, 2341, 2413, 2431, 2779, 2797, 2977, 3124, 3142, 3214, 3241, 3412, 3421, 4123, 4132, 4213, 4231, 4312, 4321]$$

$$250=[4, 13, 25, 28, 31, 40, 46, 52, 64, 82, 103, 130, 205, 208, 250, 256, 265, 280, 289, 298, 301, 310, 349, 394, 400, 406, 439, 448, 460, 484, 493, 502, 520, 526, 562, 589, 598, 604, 625, 640, 652, 802, 820, 829, 844, 859, 892, 895, 928, 934, 943, 958, 982, 985, 1003, 1030, 1111, 1144, 1222, 1246, 1249, 1264, 1294, 1300, 1333, 1348, 1366, 1384, 1414, 1426, 1429, 1438, 1441, 1456, 1462, 1465, 1483, 1492, 1546, 1564, 1624, 1636, 1642, 1645, 1654, 1663, 1777, 1834, 1843, 1924, 1942, 2005, 2008, 2050, 2056, 2065, 2080, 2089, 2098, 2122, 2146, 2149, 2164, 2194, 2212, 2221, 2245, 2254, 2257, 2266, 2275, 2416, 2419, 2425, 2452, 2461, 2479, 2491, 2497, 2500, 2506, 2524, 2527, 2542, 2560, 2572, 2605, 2614, 2626, 2641, 2650, 2662, 2689, 2698, 2725, 2749, 2752, 2794, 2800, 2809, 2869, 2890, 2896, 2908, 2914, 2941, 2947, 2968, 2974, 2980, 2986, 3001, 3010, 3049, 3094, 3100, 3133, 3148, 3166, 3184, 3313, 3331, 3409, 3418, 3445, 3454, 3481, 3490, 3544, 3556, 3565, 3616, 3655, 3661, 3667, 3676, 3766, 3814, 3841, 3904, 3940, 4000, 4006, 4039, 4048, 4060, 4084, 4093, 4114, 4126, 4129, 4138, 4141, 4156, 4162, 4165, 4183, 4192, 4216, 4219, 4225, 4252, 4261, 4279, 4291, 4297, 4309, 4318, 4345, 4354, 4381, 4390, 4408, 4411, 4435, 4444, 4453, 4459, 4480, 4495, 4516, 4522, 4534, 4543, 4549, 4555, 4561, 4594, 4600, 4612, 4615, 4621, 4651, 4729, 4792, 4804, 4813, 4831, 4840, 4903, 4912, 4921, 4927, 4930, 4945, 4954, 4972]$$

$$370=[7, 19, 34, 37, 43, 58, 67, 70, 73, 76, 85, 88, 91, 109, 118, 124, 139, 142, 145, 148, 154, 157, 166, 169, 175, 178, 181, 184, 187, 190, 193, 196, 214, 223, 226, 232, 241, 247, 259, 262, 268, 274, 277, 286, 295, 304, 307, 319, 322, 334, 340, 343, 346, 355, 358, 364, 367, 370, 376, 385, 391, 403, 412, 415, 418, 421, 427, 430, 433, 436, 451, 463, 466, 469, 472, 481, 496, 499, 508, 514, 517, 529, 535, 538, 541, 553, 556, 559, 565, 568, 571, 577, 580, 583, 586, 592, 595, 607, 616, 619, 622, 628, 634, 637, 643, 646, 649, 655, 658, 661, 664, 667, 670, 673, 676, 682, 685, 688, 691, 694, 700, 703, 706, 715, 718, 724, 727, 730, 736, 742, 751, 757, 760, 763, 766, 772, 775, 781, 799, 805, 808, 811, 814, 817, 826, 835, 841, 850, 853, 856, 862, 865, 868, 871, 880, 886, 889, 898, 901, 910, 913, 916, 925, 931, 946, 949, 952, 955, 961, 964, 979, 988, 994, 997, 1009, 1018, 1024, 1039, 1042, 1045, 1048, 1054, 1057, 1066, 1069, 1075, 1078, 1081, 1084, 1087, 1090, 1093, 1096, 1108, 1114, 1117, 1123, 1126, 1132, 1135, 1138, 1141, 1153, 1156, 1159, 1162, 1165, 1168, 1171, 1177, 1180, 1183, 1186, 1195, 1204, 1213, 1216, 1225, 1228, 1231, 1240, 1252, 1255, 1258, 1261, 1267, 1276, 1279, 1282, 1285, 1297, 1309, 1312, 1315, 1318, 1321, 1351, 1357, 1375, 1381, 1390, 1402, 1405, 1408, 1411, 1420, 1444, 1447, 1450, 1474, 1477, 1480, 1504, 1507, 1513, 1516, 1519, 1522, 1525, 1528, 1531, 1537, 1540, 1552, 1555, 1558, 1561, 1567, 1570, 1573, 1576, 1582, 1585, 1591, 1606, 1609, 1612, 1615, 1618, 1621, 1627, 1651, 1657, 1660, 1666, 1669, 1672, 1675, 1681, 1690, 1696, 1699, 1705, 1708, 1711, 1717, 1726, 1729, 1735, 1744, 1747, 1750, 1753, 1756, 1762, 1765, 1771, 1774, 1780, 1789, 1792, 1798, 1801, 1804, 1807, 1810, 1813, 1816, 1822, 1825, 1831, 1840, 1852, 1855, 1861, 1870, 1879, 1888, 1897, 1900, 1903, 1906, 1915, 1927, 1930, 1951, 1960, 1966, 1969, 1972, 1978, 1987, 1996, 2014, 2023, 2026, 2032, 2041, 2047, 2059, 2062, 2068, 2074, 2077, 2086, 2095, 2104, 2113, 2116, 2125, 2128, 2131, 2140, 2152, 2155, 2158, 2161, 2167, 2176, 2179, 2182, 2185, 2197, 2203, 2206, 2215, 2218, 2224, 2227, 2230, 2233, 2236, 2239, 2242, 2248, 2251, 2260, 2263, 2269, 2272, 2278, 2281, 2284, 2287, 2293, 2296, 2299, 2302, 2311, 2320, 2323, 2326, 2329, 2332, 2335, 2353, 2356, 2359, 2362, 2365, 2368, 2386, 2389, 2392, 2395, 2398, 2401, 2407, 2410, 2422, 2428, 2449, 2455, 2470, 2482, 2488, 2494, 2509, 2512, 2515, 2518, 2521, 2533, 2536, 2539, 2545, 2551, 2554, 2563, 2566, 2569, 2578, 2581, 2587, 2590, 2593, 2596, 2599, 2602, 2608, 2611, 2617, 2620, 2623, 2629, 2632, 2635, 2638, 2653, 2656, 2659, 2665, 2668, 2671, 2677, 2680, 2683, 2686, 2692, 2695, 2704, 2707, 2716, 2719, 2722, 2728, 2740, 2758, 2761, 2767, 2770, 2776, 2782, 2785, 2788, 2791, 2806, 2812, 2815, 2821, 2824, 2827, 2836, 2839, 2842, 2848, 2851, 2857, 2860, 2863, 2866, 2872, 2875, 2878, 2884, 2887, 2893, 2899, 2905, 2917, 2923, 2926, 2929, 2932, 2935, 2938, 2944, 2950, 2953, 2956, 2959, 2962, 2965, 2971, 2983, 2989, 2992, 2995, 2998, 3004, 3007, 3019, 3022, 3034, 3040, 3043, 3046, 3055, 3058, 3064, 3067, 3070, 3076, 3085, 3091, 3109, 3112, 3115, 3118, 3121, 3151, 3157, 3175, 3181, 3190, 3202, 3211, 3220, 3223, 3226, 3229, 3232, 3235, 3253, 3256, 3259, 3262, 3265, 3268, 3286, 3289, 3292, 3295, 3298, 3304, 3322, 3325, 3334, 3340, 3343, 3346, 3352, 3355, 3358, 3364, 3379, 3385, 3388, 3397, 3400, 3403, 3406, 3430, 3433, 3436, 3448, 3457, 3460, 3463, 3475, 3478, 3484, 3487, 3505, 3508, 3511, 3517, 3523, 3526, 3529, 3532, 3535, 3538, 3547, 3550, 3553, 3562, 3568, 3571, 3574, 3580, 3583, 3586, 3592, 3604, 3607, 3622, 3625, 3628, 3634, 3640, 3643, 3652, 3658, 3670, 3679, 3682, 3685, 3688, 3697, 3700, 3706, 3715, 3739, 3745, 3748, 3751, 3754, 3760, 3769, 3778, 3784, 3787, 3793, 3796, 3805, 3811, 3826, 3829, 3835, 3838, 3844, 3847, 3850, 3853, 3856, 3862, 3865, 3868, 3874, 3877, 3883, 3886, 3889, 3892, 3898, 3901, 3910, 3922, 3925, 3928, 3937, 3952, 3967, 3973, 3976, 3982, 3988, 4003, 4012, 4015, 4018, 4021, 4027, 4030, 4033, 4036, 4051, 4063, 4066, 4069, 4072, 4081, 4096, 4099, 4102, 4105, 4108, 4111, 4120, 4144, 4147, 4150, 4174, 4177, 4180, 4201, 4207, 4210, 4222, 4228, 4249, 4255, 4270, 4282, 4288, 4294, 4300, 4303, 4306, 4330, 4333, 4336, 4348, 4357, 4360, 4363, 4375, 4378, 4384, 4387, 4414, 4417, 4429, 4438, 4441, 4447, 4456, 4465, 4468, 4471, 4474, 4477, 4483, 4486, 4492, 4501, 4510, 4525, 4537, 4546, 4552, 4558, 4564, 4573, 4579, 4585, 4588, 4597, 4603, 4606, 4609, 4630, 4633, 4645, 4648, 4654, 4660, 4669, 4678, 4684, 4687, 4690, 4696, 4702, 4714, 4717, 4720, 4735, 4738, 4741, 4744, 4747, 4753, 4759, 4768, 4771, 4774, 4777, 4783, 4786, 4795, 4801, 4810, 4822, 4828, 4834, 4837, 4843, 4846, 4855, 4858, 4864, 4867, 4873, 4876, 4882, 4885, 4906, 4909, 4924, 4942, 4957, 4960, 4966, 4975, 4990, 4999]$$
$$160=[16, 22, 61, 106, 160, 202, 220, 601, 610, 1006, 1060, 1345, 1354, 1435, 1453, 1534, 1543, 1600, 2002, 2020, 2200, 2557, 2575, 2755, 3145, 3154, 3415, 3451, 3514, 3541, 3559, 3595, 3955, 4135, 4153, 4315, 4351, 4513, 4531, 4888]$$
$$407=[47, 74, 77, 89, 98, 407, 449, 470, 494, 578, 587, 668, 686, 704, 707, 740, 758, 770, 785, 788, 809, 857, 866, 875, 878, 887, 890, 908, 944, 980, 1124, 1139, 1142, 1148, 1157, 1175, 1178, 1184, 1187, 1193, 1214, 1241, 1319, 1367, 1376, 1391, 1412, 1418, 1421, 1481, 1517, 1559, 1571, 1589, 1595, 1598, 1637, 1673, 1688, 1715, 1718, 1736, 1751, 1763, 1781, 1814, 1817, 1841, 1859, 1868, 1871, 1886, 1895, 1913, 1931, 1955, 1958, 1985, 2114, 2141, 2249, 2294, 2333, 2369, 2378, 2387, 2396, 2411, 2429, 2477, 2492, 2558, 2585, 2588, 2639, 2693, 2738, 2747, 2774, 2783, 2837, 2855, 2858, 2873, 2885, 2924, 2936, 2942, 2963, 3119, 3167, 3176, 3191, 3233, 3269, 3278, 3287, 3296, 3323, 3332, 3359, 3377, 3395, 3539, 3593, 3617, 3629, 3671, 3692, 3716, 3728, 3737, 3761, 3773, 3782, 3827, 3872, 3911, 3926, 3935, 3953, 3962, 4007, 4049, 4070, 4094, 4112, 4118, 4121, 4181, 4211, 4229, 4277, 4292, 4409, 4448, 4484, 4490, 4577, 4700, 4727, 4757, 4772, 4775, 4811, 4844, 4889, 4898, 4904, 4922, 4940, 4988]$$
$$55=[55, 505, 550]$$
$$217=[79, 97, 115, 127, 151, 172, 217, 271, 388, 511, 709, 712, 721, 790, 838, 883, 907, 970, 1015, 1027, 1051, 1072, 1105, 1150, 1207, 1270, 1336, 1363, 1378, 1387, 1501, 1510, 1588, 1633, 1678, 1687, 1702, 1720, 1738, 1768, 1783, 1786, 1837, 1858, 1867, 1873, 1876, 1885, 2017, 2071, 2107, 2170, 2377, 2446, 2458, 2464, 2485, 2548, 2584, 2644, 2701, 2710, 2737, 2773, 2845, 2854, 3088, 3136, 3163, 3178, 3187, 3277, 3316, 3361, 3577, 3613, 3631, 3718, 3727, 3757, 3772, 3775, 3781, 3808, 3817, 3871, 3880, 4246, 4258, 4264, 4285, 4426, 4462, 4528, 4582, 4624, 4642, 4666, 4699, 4825, 4852, 4969, 4996]$$
$$133=[133, 313, 331, 679, 697, 769, 796, 967, 976, 1033, 1288, 1303, 1330, 1828, 1882, 1999, 2188, 2818, 2881, 3013, 3031, 3103, 3130, 3301, 3310, 3799, 3979, 3997]$$
$$352=[229, 235, 238, 253, 283, 292, 325, 328, 352, 382, 445, 454, 457, 475, 523, 532, 544, 547, 574, 745, 754, 823, 832, 922, 2029, 2035, 2038, 2053, 2083, 2092, 2209, 2290, 2305, 2308, 2338, 2350, 2380, 2383, 2503, 2530, 2803, 2830, 2833, 2902, 2920, 3025, 3028, 3052, 3082, 3205, 3208, 3238, 3250, 3280, 3283, 3328, 3382, 3466, 3502, 3520, 3646, 3664, 3802, 3820, 3823, 3832, 4045, 4054, 4057, 4075, 4366, 4405, 4450, 4504, 4507, 4540, 4570, 4636, 4663, 4705, 4750]$$
$$244=[244, 424, 442, 2044, 2347, 2374, 2404, 2437, 2440, 2473, 2734, 2743, 3247, 3274, 3337, 3373, 3427, 3472, 3724, 3733, 3742, 4024, 4042, 4204, 4237, 4240, 4273, 4327, 4372, 4402, 4420, 4723, 4732]$$

$$371=[2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 50, 53, 56, 59, 62, 65, 68, 71, 80, 83, 86, 92, 95, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, 146, 149, 152, 155, 158, 161, 164, 167, 170, 173, 176, 179, 182, 185, 188, 191, 194, 197, 200, 203, 206, 209, 212, 215, 218, 221, 224, 227, 230, 233, 236, 239, 242, 245, 248, 251, 254, 257, 260, 263, 266, 269, 272, 275, 278, 281, 284, 287, 290, 293, 296, 299, 302, 305, 308, 311, 314, 317, 320, 323, 326, 329, 332, 335, 338, 341, 344, 347, 350, 353, 356, 359, 362, 365, 368, 371, 374, 377, 380, 383, 386, 389, 392, 395, 398, 401, 404, 410, 413, 416, 419, 422, 425, 428, 431, 434, 437, 440, 443, 446, 452, 455, 458, 461, 464, 467, 473, 476, 479, 482, 485, 488, 491, 497, 500, 503, 506, 509, 512, 515, 518, 521, 524, 527, 530, 533, 536, 539, 542, 545, 548, 551, 554, 557, 560, 563, 566, 569, 572, 575, 581, 584, 590, 593, 596, 599, 602, 605, 608, 611, 614, 617, 620, 623, 626, 629, 632, 635, 638, 641, 644, 647, 650, 653, 656, 659, 662, 665, 671, 674, 677, 680, 683, 689, 692, 695, 698, 701, 710, 713, 716, 719, 722, 725, 728, 731, 734, 737, 743, 746, 749, 752, 755, 761, 764, 767, 773, 776, 779, 782, 791, 794, 797, 800, 803, 806, 812, 815, 818, 821, 824, 827, 830, 833, 836, 839, 842, 845, 848, 851, 854, 860, 863, 869, 872, 881, 884, 893, 896, 899, 902, 905, 911, 914, 917, 920, 923, 926, 929, 932, 935, 938, 941, 947, 950, 953, 956, 959, 962, 965, 968, 971, 974, 977, 983, 986, 989, 992, 995, 998, 1001, 1004, 1007, 1010, 1013, 1016, 1019, 1022, 1025, 1028, 1031, 1034, 1037, 1040, 1043, 1046, 1049, 1052, 1055, 1058, 1061, 1064, 1067, 1070, 1073, 1076, 1079, 1082, 1085, 1088, 1091, 1094, 1097, 1100, 1103, 1106, 1109, 1112, 1115, 1118, 1121, 1127, 1130, 1133, 1136, 1145, 1151, 1154, 1160, 1163, 1166, 1169, 1172, 1181, 1190, 1196, 1199, 1202, 1205, 1208, 1211, 1217, 1220, 1223, 1226, 1229, 1232, 1235, 1238, 1244, 1247, 1250, 1253, 1256, 1259, 1262, 1265, 1268, 1271, 1274, 1277, 1280, 1283, 1286, 1289, 1292, 1295, 1298, 1301, 1304, 1307, 1310, 1313, 1316, 1322, 1325, 1328, 1331, 1334, 1337, 1340, 1343, 1346, 1349, 1352, 1355, 1358, 1361, 1364, 1370, 1373, 1379, 1382, 1385, 1388, 1394, 1397, 1400, 1403, 1406, 1409, 1415, 1424, 1427, 1430, 1433, 1436, 1439, 1442, 1445, 1448, 1451, 1454, 1457, 1460, 1463, 1466, 1469, 1472, 1475, 1478, 1484, 1487, 1490, 1493, 1496, 1499, 1502, 1505, 1508, 1511, 1514, 1520, 1523, 1526, 1529, 1532, 1535, 1538, 1541, 1544, 1547, 1550, 1553, 1556, 1562, 1565, 1568, 1574, 1577, 1580, 1583, 1586, 1592, 1601, 1604, 1607, 1610, 1613, 1616, 1619, 1622, 1625, 1628, 1631, 1634, 1640, 1643, 1646, 1649, 1652, 1655, 1658, 1661, 1664, 1667, 1670, 1676, 1679, 1682, 1685, 1691, 1694, 1697, 1700, 1703, 1706, 1709, 1712, 1721, 1724, 1727, 1730, 1733, 1739, 1742, 1745, 1748, 1754, 1757, 1760, 1766, 1769, 1772, 1775, 1778, 1784, 1787, 1790, 1793, 1796, 1799, 1802, 1805, 1808, 1811, 1820, 1823, 1826, 1829, 1832, 1835, 1838, 1844, 1847, 1850, 1853, 1856, 1862, 1865, 1874, 1877, 1880, 1883, 1889, 1892, 1898, 1901, 1904, 1907, 1910, 1916, 1919, 1922, 1925, 1928, 1934, 1937, 1940, 1943, 1946, 1949, 1952, 1961, 1964, 1967, 1970, 1973, 1976, 1979, 1982, 1988, 1991, 1994, 1997, 2000, 2003, 2006, 2009, 2012, 2015, 2018, 2021, 2024, 2027, 2030, 2033, 2036, 2039, 2042, 2045, 2048, 2051, 2054, 2057, 2060, 2063, 2066, 2069, 2072, 2075, 2078, 2081, 2084, 2087, 2090, 2093, 2096, 2099, 2102, 2105, 2108, 2111, 2117, 2120, 2123, 2126, 2129, 2132, 2135, 2138, 2144, 2147, 2150, 2153, 2156, 2159, 2162, 2165, 2168, 2171, 2174, 2177, 2180, 2183, 2186, 2189, 2192, 2195, 2198, 2201, 2204, 2207, 2210, 2213, 2216, 2219, 2222, 2225, 2228, 2231, 2234, 2237, 2240, 2243, 2246, 2252, 2255, 2258, 2261, 2264, 2267, 2270, 2273, 2276, 2279, 2282, 2285, 2288, 2291, 2297, 2300, 2303, 2306, 2309, 2312, 2315, 2318, 2321, 2324, 2327, 2330, 2336, 2339, 2342, 2345, 2348, 2351, 2354, 2357, 2360, 2363, 2366, 2372, 2375, 2381, 2384, 2390, 2393, 2399, 2402, 2405, 2408, 2414, 2417, 2420, 2423, 2426, 2432, 2435, 2438, 2441, 2444, 2447, 2450, 2453, 2456, 2459, 2462, 2465, 2468, 2471, 2474, 2480, 2483, 2486, 2489, 2495, 2498, 2501, 2504, 2507, 2510, 2513, 2516, 2519, 2522, 2525, 2528, 2531, 2534, 2537, 2540, 2543, 2546, 2549, 2552, 2555, 2561, 2564, 2567, 2570, 2573, 2576, 2579, 2582, 2591, 2594, 2597, 2600, 2603, 2606, 2609, 2612, 2615, 2618, 2621, 2624, 2627, 2630, 2633, 2636, 2642, 2645, 2648, 2651, 2654, 2657, 2660, 2663, 2666, 2669, 2672, 2675, 2678, 2681, 2684, 2687, 2690, 2696, 2699, 2702, 2705, 2708, 2711, 2714, 2717, 2720, 2723, 2726, 2729, 2732, 2735, 2741, 2744, 2750, 2753, 2756, 2759, 2762, 2765, 2768, 2771, 2777, 2780, 2786, 2789, 2792, 2795, 2798, 2801, 2804, 2807, 2810, 2813, 2816, 2819, 2822, 2825, 2828, 2831, 2834, 2840, 2843, 2846, 2849, 2852, 2861, 2864, 2867, 2870, 2876, 2879, 2882, 2888, 2891, 2894, 2897, 2900, 2903, 2906, 2909, 2912, 2915, 2918, 2921, 2927, 2930, 2933, 2939, 2945, 2948, 2951, 2954, 2957, 2960, 2966, 2969, 2972, 2975, 2978, 2981, 2984, 2987, 2990, 2993, 2996, 2999, 3002, 3005, 3008, 3011, 3014, 3017, 3020, 3023, 3026, 3029, 3032, 3035, 3038, 3041, 3044, 3047, 3050, 3053, 3056, 3059, 3062, 3065, 3068, 3071, 3074, 3077, 3080, 3083, 3086, 3089, 3092, 3095, 3098, 3101, 3104, 3107, 3110, 3113, 3116, 3122, 3125, 3128, 3131, 3134, 3137, 3140, 3143, 3146, 3149, 3152, 3155, 3158, 3161, 3164, 3170, 3173, 3179, 3182, 3185, 3188, 3194, 3197, 3200, 3203, 3206, 3209, 3212, 3215, 3218, 3221, 3224, 3227, 3230, 3236, 3239, 3242, 3245, 3248, 3251, 3254, 3257, 3260, 3263, 3266, 3272, 3275, 3281, 3284, 3290, 3293, 3299, 3302, 3305, 3308, 3311, 3314, 3317, 3320, 3326, 3329, 3335, 3338, 3341, 3344, 3347, 3350, 3353, 3356, 3362, 3365, 3368, 3371, 3374, 3380, 3383, 3386, 3389, 3392, 3398, 3401, 3404, 3407, 3410, 3413, 3416, 3419, 3422, 3425, 3428, 3431, 3434, 3437, 3440, 3443, 3446, 3449, 3452, 3455, 3458, 3461, 3464, 3467, 3470, 3473, 3476, 3479, 3482, 3485, 3488, 3491, 3494, 3497, 3500, 3503, 3506, 3509, 3512, 3515, 3518, 3521, 3524, 3527, 3530, 3533, 3536, 3542, 3545, 3548, 3551, 3554, 3557, 3560, 3563, 3566, 3569, 3572, 3575, 3578, 3581, 3584, 3587, 3590, 3596, 3599, 3602, 3605, 3608, 3611, 3614, 3620, 3623, 3626, 3632, 3635, 3638, 3641, 3644, 3647, 3650, 3653, 3656, 3659, 3662, 3665, 3668, 3674, 3677, 3680, 3683, 3686, 3689, 3695, 3698, 3701, 3704, 3707, 3710, 3713, 3719, 3722, 3725, 3731, 3734, 3740, 3743, 3746, 3749, 3752, 3755, 3758, 3764, 3767, 3770, 3776, 3779, 3785, 3788, 3791, 3794, 3797, 3800, 3803, 3806, 3809, 3812, 3815, 3818, 3821, 3824, 3830, 3833, 3836, 3839, 3842, 3845, 3848, 3851, 3854, 3857, 3860, 3863, 3866, 3869, 3875, 3878, 3881, 3884, 3887, 3890, 3893, 3896, 3899, 3902, 3905, 3908, 3914, 3917, 3920, 3923, 3929, 3932, 3938, 3941, 3944, 3947, 3950, 3956, 3959, 3965, 3968, 3971, 3974, 3977, 3980, 3983, 3986, 3989, 3992, 3995, 3998, 4001, 4004, 4010, 4013, 4016, 4019, 4022, 4025, 4028, 4031, 4034, 4037, 4040, 4043, 4046, 4052, 4055, 4058, 4061, 4064, 4067, 4073, 4076, 4079, 4082, 4085, 4088, 4091, 4097, 4100, 4103, 4106, 4109, 4115, 4124, 4127, 4130, 4133, 4136, 4139, 4142, 4145, 4148, 4151, 4154, 4157, 4160, 4163, 4166, 4169, 4172, 4175, 4178, 4184, 4187, 4190, 4193, 4196, 4199, 4202, 4205, 4208, 4214, 4217, 4220, 4223, 4226, 4232, 4235, 4238, 4241, 4244, 4247, 4250, 4253, 4256, 4259, 4262, 4265, 4268, 4271, 4274, 4280, 4283, 4286, 4289, 4295, 4298, 4301, 4304, 4307, 4310, 4313, 4316, 4319, 4322, 4325, 4328, 4331, 4334, 4337, 4340, 4343, 4346, 4349, 4352, 4355, 4358, 4361, 4364, 4367, 4370, 4373, 4376, 4379, 4382, 4385, 4388, 4391, 4394, 4397, 4400, 4403, 4406, 4412, 4415, 4418, 4421, 4424, 4427, 4430, 4433, 4436, 4439, 4442, 4445, 4451, 4454, 4457, 4460, 4463, 4466, 4469, 4472, 4475, 4478, 4481, 4487, 4493, 4496, 4499, 4502, 4505, 4508, 4511, 4514, 4517, 4520, 4523, 4526, 4529, 4532, 4535, 4538, 4541, 4544, 4547, 4550, 4553, 4556, 4559, 4562, 4565, 4568, 4571, 4574, 4580, 4583, 4586, 4589, 4592, 4595, 4598, 4601, 4604, 4607, 4610, 4613, 4616, 4619, 4622, 4625, 4628, 4631, 4634, 4637, 4640, 4643, 4646, 4649, 4652, 4655, 4658, 4661, 4664, 4667, 4670, 4673, 4676, 4679, 4682, 4685, 4688, 4691, 4694, 4697, 4703, 4706, 4709, 4712, 4715, 4718, 4721, 4724, 4730, 4733, 4736, 4739, 4742, 4745, 4748, 4751, 4754, 4760, 4763, 4766, 4769, 4778, 4781, 4784, 4787, 4790, 4793, 4796, 4799, 4802, 4805, 4808, 4814, 4817, 4820, 4823, 4826, 4829, 4832, 4835, 4838, 4841, 4847, 4850, 4853, 4856, 4859, 4862, 4865, 4868, 4871, 4874, 4877, 4880, 4883, 4886, 4892, 4895, 4901, 4907, 4910, 4913, 4916, 4919, 4925, 4928, 4931, 4934, 4937, 4943, 4946, 4949, 4952, 4955, 4958, 4961, 4964, 4967, 4970, 4973, 4976, 4979, 4982, 4985, 4991, 4994, 4997]$$