/*
    Copyright (C) 2019 Alessandro Languasco
*/

{greedy()=local(A, L, B, n, v , ok , R, setR, p, k);
A=vector(2090); \\ 2089 is the length to get sum(1/A[i])>2; escluso il primo termine banale
L=length(A);
B = 10^(5); 
A[1]=0;
for (n=2, L, 
		R=vector(n); 
		forstep (v=A[n-1]+2, B, 2 , ok=1;
			            forprime(p = 2, v, 
			                for(k=1,n-1, R[k]=A[k]%p);
			                R[n]=v%p; 
				            setR=Set(R); 
				            if (length(setR) > p-1, ok=0; break);
				         );
		        if (ok==1, A[n]=v; break);
		        ); 
	);
print(length(A));
return(A)
}

/*

air:Desktop languasc$ gp2c-run -pmy_ -g -W greedy_seq.gp 

GP/PARI CALCULATOR Version 2.11.1 (released)
i386 running darwin (x86-64/GMP-6.1.2 kernel) 64-bit version
compiled: Dec  2 2018, Apple LLVM version 10.0.0 (clang-1000.11.45.5)
threading engine: single
(readline v6.3 enabled, extended help enabled)
Copyright (C) 2000-2018 The PARI Group

PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER.

Type ? for help, \q to quit.
Type ?17 for how to get moral (and possibly technical) support.

parisize = 8000000, primelimit = 500000
? greedy()
 
%2 = [0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50, 56, 62, 68, 72, 78,
%86, 90, 96, 98, 102, 110, 116, 120, 128, 132, 138, 140, 146, 152, 156, 158,
%162, 168, 176, 182, 186, 188, 198, 200, 210, 212, 216, 230, 240, 242, 246, 252,
%260, 266, 270, 272, 278, 282, 288, 306, 308, 312, 320, 336, 338, 342, 348, 350,
%362, 372, 380, 386, 392, 396, 410, 420, 422, 426, 428, 438, 450, 452, 462, 468,
%470, 476, 488, 492, 498, 506, 510, 512, 516, 530, 536, 548, 552, 558, 572, 578,
%582, 590, 596, 600, 606, 608, 618, 620, 630, 642, 648, 650, 656, 660, 672, 680,
%686, 702, 708, 722, 726, 732, 740, 746, 756, 758, 762, 776, 782, 798, 800, 812,
%818, 828, 842, 848, 858, 860, 870, 876, 882, 888, 890, 900, 912, 926, 930, 936,
%938, 960, 966, 968, 972, 980, 986, 992, 996, 998, 1008, 1020, 1022, 1026, 1052,
%1056, 1058, 1062, 1068, 1070, 1076, 1082, 1086, 1110, 1118, 1122, 1128, 1136,
%1140, 1142, 1148, 1152, 1166, 1170, 1176, 1178, 1188, 1190, 1196, 1208, 1212,
%1218, 1220, 1232, 1238, 1260, 1266, 1278, 1280, 1290, 1296, 1302, 1308, 1310,
%1332, 1338, 1346, 1352, 1362, 1370, 1376, 1398, 1400, 1406, 1412, 1416, 1428,
%1430, 1436, 1442, 1458, 1478, 1488, 1500, 1502, 1518, 1532, 1538, 1542, 1560,
%1566, 1572, 1580, 1590, 1602, 1608, 1610, 1616, 1628, 1632, 1640, 1646, 1650,
%1670, 1680, 1682, 1686, 1706, 1712, 1716, 1722, 1728, 1742, 1748, 1752, 1766,
%1770, 1778, 1790, 1796, 1800, 1806, 1812, 1818, 1832, 1836, 1848, 1850, 1862,
%1866, 1868, 1878, 1880, 1892, 1896, 1898, 1902, 1916, 1922, 1926, 1946, 1958,
%1980, 1982, 1986, 1988, 2000, 2010, 2028, 2036, 2046, 2052, 2060, 2066, 2070,
%2072, 2076, 2078, 2088, 2090, 2100, 2102, 2108, 2112, 2130, 2136, 2148, 2160,
%2162, 2168, 2178, 2190, 2192, 2202, 2210, 2220, 2226, 2228, 2240, 2246, 2252,
%2256, 2262, 2280, 2286, 2312, 2318, 2322, 2342, 2352, 2358, 2360, 2366, 2382,
%2388, 2396, 2400, 2408, 2412, 2430, 2442, 2450, 2456, 2462, 2466, 2468, 2478,
%2486, 2496, 2508, 2528, 2532, 2552, 2556, 2570, 2576, 2580, 2582, 2592, 2598,
%2616, 2618, 2622, 2636, 2648, 2658, 2672, 2682, 2690, 2696, 2706, 2708, 2720,
%2732, 2738, 2742, 2750, 2756, 2762, 2772, 2786, 2790, 2792, 2798, 2820, 2826,
%2828, 2850, 2856, 2862, 2868, 2870, 2888, 2892, 2910, 2912, 2918, 2928, 2930,
%2940, 2958, 2966, 2970, 2972, 2976, 2990, 2996, 3002, 3026, 3032, 3036, 3042,
%3060, 3066, 3072, 3086, 3092, 3098, 3110, 3122, 3126, 3138, 3150, 3168, 3176,
%3180, 3192, 3198, 3200, 3210, 3222, 3236, 3240, 3242, 3260, 3276, 3282, 3308,
%3312, 3318, 3330, 3336, 3348, 3350, 3362, 3366, 3378, 3380, 3386, 3396, 3402,
%3408, 3422, 3428, 3432, 3452, 3462, 3480, 3488, 3500, 3506, 3512, 3516, 3522,
%3528, 3540, 3542, 3570, 3578, 3588, 3596, 3606, 3620, 3626, 3630, 3632, 3648,
%3660, 3666, 3672, 3686, 3698, 3702, 3710, 3716, 3722, 3726, 3728, 3738, 3740,
%3768, 3780, 3782, 3786, 3788, 3792, 3812, 3816, 3840, 3842, 3858, 3870, 3876,
%3878, 3896, 3906, 3912, 3920, 3926, 3936, 3938, 3948, 3950, 3960, 3962, 3978,
%3996, 4008, 4010, 4022, 4026, 4032, 4038, 4040, 4046, 4052, 4058, 4062, 4080,
%4088, 4092, 4110, 4116, 4118, 4136, 4146, 4158, 4160, 4166, 4176, 4178, 4188,
%4190, 4202, 4212, 4232, 4242, 4248, 4250, 4256, 4260, 4268, 4272, 4286, 4292,
%4296, 4298, 4302, 4310, 4316, 4320, 4326, 4332, 4338, 4352, 4368, 4370, 4380,
%4412, 4418, 4422, 4428, 4442, 4446, 4452, 4458, 4466, 4470, 4472, 4500, 4502,
%4506, 4530, 4556, 4562, 4568, 4586, 4596, 4598, 4608, 4620, 4628, 4632, 4638,
%4640, 4652, 4670, 4692, 4698, 4706, 4712, 4718, 4722, 4730, 4736, 4766, 4776,
%4782, 4788, 4796, 4800, 4802, 4830, 4836, 4842, 4848, 4860, 4862, 4866, 4872,
%4890, 4898, 4908, 4916, 4940, 4946, 4950, 4970, 4976, 4982, 4986, 4992, 4998,
%5012, 5018, 5030, 5040, 5046, 5060, 5070, 5088, 5096, 5108, 5118, 5126, 5132,
%5150, 5156, 5160, 5166, 5168, 5178, 5198, 5202, 5210, 5222, 5228, 5238, 5256,
%5258, 5262, 5268, 5276, 5282, 5286, 5300, 5306, 5312, 5322, 5336, 5342, 5352,
%5376, 5382, 5388, 5402, 5408, 5412, 5418, 5426, 5432, 5438, 5468, 5478, 5480,
%5486, 5492, 5496, 5520, 5528, 5550, 5556, 5558, 5562, 5570, 5580, 5586, 5588,
%5592, 5598, 5606, 5612, 5618, 5628, 5636, 5640, 5642, 5658, 5672, 5676, 5678,
%5696, 5700, 5706, 5718, 5720, 5726, 5730, 5732, 5742, 5748, 5756, 5762, 5772,
%5790, 5798, 5810, 5816, 5822, 5828, 5832, 5840, 5850, 5852, 5856, 5858, 5882,
%5886, 5888, 5892, 5900, 5910, 5952, 5966, 5976, 5982, 6006, 6026, 6036, 6038,
%6048, 6050, 6056, 6062, 6068, 6078, 6080, 6090, 6092, 6096, 6102, 6116, 6120,
%6140, 6162, 6168, 6182, 6186, 6188, 6192, 6200, 6206, 6210, 6216, 6218, 6230,
%6236, 6248, 6252, 6258, 6272, 6276, 6278, 6300, 6302, 6312, 6320, 6326, 6350,
%6356, 6362, 6372, 6378, 6390, 6392, 6420, 6426, 6446, 6452, 6456, 6458, 6468,
%6476, 6480, 6486, 6498, 6500, 6512, 6516, 6522, 6530, 6536, 6542, 6546, 6558,
%6560, 6570, 6588, 6606, 6626, 6630, 6636, 6642, 6662, 6668, 6672, 6690, 6692,
%6698, 6708, 6710, 6720, 6728, 6732, 6738, 6740, 6752, 6768, 6776, 6788, 6798,
%6806, 6810, 6812, 6816, 6818, 6846, 6848, 6876, 6890, 6896, 6900, 6908, 6918,
%6920, 6936, 6938, 6948, 6950, 6962, 6966, 6972, 6978, 6986, 6992, 6998, 7002,
%7016, 7022, 7040, 7046, 7076, 7082, 7088, 7098, 7110, 7140, 7146, 7152, 7160,
%7170, 7182, 7196, 7200, 7208, 7212, 7218, 7226, 7230, 7236, 7260, 7272, 7278,
%7280, 7296, 7310, 7316, 7326, 7328, 7338, 7340, 7350, 7358, 7370, 7376, 7380,
%7382, 7392, 7406, 7410, 7412, 7418, 7422, 7442, 7446, 7448, 7466, 7482, 7488,
%7506, 7508, 7512, 7520, 7526, 7530, 7550, 7560, 7566, 7568, 7586, 7592, 7596,
%7602, 7608, 7620, 7622, 7638, 7646, 7656, 7662, 7686, 7688, 7698, 7706, 7722,
%7728, 7730, 7740, 7746, 7748, 7770, 7772, 7800, 7802, 7806, 7812, 7820, 7830,
%7832, 7838, 7842, 7862, 7880, 7886, 7896, 7898, 7902, 7908, 7910, 7922, 7938,
%7950, 7952, 7956, 7986, 7998, 8010, 8012, 8028, 8030, 8036, 8040, 8042, 8066,
%8072, 8076, 8096, 8108, 8118, 8120, 8132, 8142, 8162, 8166, 8180, 8192, 8202,
%8208, 8216, 8220, 8238, 8240, 8250, 8276, 8280, 8300, 8306, 8316, 8322, 8328,
%8346, 8366, 8370, 8372, 8378, 8390, 8402, 8460, 8462, 8468, 8472, 8496, 8510,
%8520, 8526, 8528, 8532, 8538, 8546, 8556, 8562, 8570, 8588, 8610, 8622, 8628,
%8630, 8642, 8652, 8658, 8666, 8678, 8688, 8700, 8708, 8736, 8738, 8742, 8748,
%8766, 8778, 8786, 8790, 8792, 8798, 8822, 8832, 8840, 8846, 8852, 8856, 8862,
%8888, 8892, 8916, 8918, 8930, 8936, 8940, 8946, 8952, 8960, 8976, 8978, 8982,
%8990, 9006, 9018, 9020, 9030, 9038, 9042, 9048, 9060, 9066, 9086, 9090, 9092,
%9116, 9120, 9122, 9126, 9128, 9132, 9150, 9158, 9162, 9176, 9198, 9206, 9210,
%9216, 9230, 9240, 9242, 9248, 9252, 9258, 9260, 9288, 9290, 9308, 9312, 9318,
%9330, 9332, 9350, 9356, 9360, 9368, 9378, 9380, 9396, 9398, 9422, 9428, 9456,
%9458, 9462, 9482, 9486, 9500, 9522, 9536, 9546, 9548, 9552, 9560, 9570, 9590,
%9596, 9606, 9618, 9626, 9632, 9636, 9638, 9650, 9662, 9666, 9668, 9672, 9678,
%9692, 9702, 9708, 9710, 9716, 9720, 9722, 9728, 9746, 9750, 9776, 9788, 9792,
%9818, 9822, 9830, 9840, 9858, 9876, 9888, 9900, 9902, 9906, 9926, 9930, 9932,
%9948, 9956, 9962, 9968, 9980, 9990, 9996, 10008, 10010, 10032, 10038, 10052,
%10068, 10080, 10082, 10100, 10106, 10110, 10112, 10116, 10142, 10148, 10166,
%10172, 10176, 10220, 10226, 10238, 10242, 10256, 10266, 10278, 10280, 10296,
%10302, 10308, 10322, 10332, 10340, 10346, 10352, 10358, 10368, 10376, 10380,
%10392, 10406, 10442, 10446, 10452, 10458, 10460, 10490, 10500, 10506, 10508,
%10512, 10520, 10526, 10536, 10542, 10548, 10562, 10572, 10602, 10616, 10626,
%10628, 10638, 10640, 10656, 10658, 10662, 10670, 10680, 10682, 10688, 10712,
%10716, 10718, 10722, 10736, 10740, 10742, 10746, 10758, 10770, 10806, 10808,
%10850, 10868, 10872, 10892, 10920, 10922, 10926, 10932, 10940, 10946, 10952,
%10956, 10962, 10968, 10970, 10976, 10980, 10992, 10998, 11018, 11030, 11036,
%11046, 11052, 11076, 11078, 11100, 11102, 11106, 11118, 11130, 11136, 11138,
%11150, 11156, 11160, 11172, 11186, 11198, 11202, 11208, 11228, 11232, 11240,
%11250, 11262, 11270, 11282, 11286, 11292, 11300, 11310, 11316, 11340, 11342,
%11348, 11358, 11372, 11382, 11388, 11408, 11418, 11430, 11432, 11436, 11438,
%11460, 11468, 11472, 11486, 11492, 11498, 11508, 11510, 11526, 11528, 11552,
%11556, 11562, 11568, 11570, 11576, 11582, 11586, 11598, 11612, 11622, 11646,
%11648, 11660, 11666, 11678, 11682, 11696, 11706, 11708, 11730, 11736, 11738,
%11768, 11772, 11778, 11790, 11816, 11832, 11838, 11858, 11880, 11898, 11900,
%11906, 11912, 11916, 11928, 11936, 11946, 11970, 11972, 11976, 11978, 11982,
%11988, 11996, 12030, 12038, 12042, 12048, 12056, 12066, 12068, 12090, 12096,
%12098, 12110, 12122, 12140, 12146, 12152, 12158, 12170, 12180, 12186, 12192,
%12200, 12210, 12212, 12216, 12228, 12240, 12258, 12266, 12282, 12296, 12300,
%12320, 12326, 12342, 12348, 12356, 12392, 12396, 12398, 12410, 12420, 12422,
%12426, 12432, 12438, 12450, 12452, 12458, 12462, 12476, 12480, 12482, 12488,
%12506, 12516, 12522, 12528, 12542, 12548, 12552, 12558, 12560, 12566, 12588,
%12590, 12612, 12626, 12630, 12642, 12648, 12656, 12660, 12662, 12668, 12678,
%12686, 12690, 12692, 12716, 12726, 12738, 12746, 12752, 12762, 12768, 12770,
%12788, 12800, 12812, 12828, 12836, 12852, 12860, 12866, 12870, 12882, 12888,
%12896, 12900, 12902, 12920, 12938, 12966, 12968, 12972, 12980, 12990, 12992,
%12998, 13008, 13022, 13026, 13032, 13056, 13070, 13076, 13088, 13110, 13112,
%13116, 13130, 13140, 13146, 13152, 13158, 13160, 13166, 13178, 13200, 13202,
%13206, 13208, 13262, 13266, 13272, 13280, 13286, 13292, 13298, 13302, 13320,
%13322, 13340, 13346, 13356, 13358, 13362, 13382, 13400, 13406, 13410, 13412,
%13416, 13448, 13460, 13470, 13490, 13496, 13526, 13530, 13532, 13536, 13542,
%13550, 13572, 13578, 13592, 13598, 13602, 13608, 13616, 13620, 13622, 13628,
%13640, 13662, 13668, 13676, 13680, 13698, 13710, 13712, 13718, 13728, 13740,
%13752, 13770, 13778, 13782, 13790, 13796, 13802, 13806, 13808, 13812, 13818,
%13826, 13836, 13848, 13866, 13868, 13878, 13892, 13922, 13932, 13946, 13958,
%13962, 13980, 13988, 13992, 14000, 14016, 14040, 14046, 14048, 14060, 14072,
%14078, 14102, 14112, 14138, 14142, 14166, 14172, 14186, 14190, 14196, 14198,
%14208, 14216, 14222, 14226, 14232, 14238, 14246, 14256, 14258, 14268, 14280,
%14282, 14286, 14292, 14300, 14310, 14312, 14330, 14342, 14348, 14370, 14378,
%14390, 14396, 14408, 14412, 14436, 14442, 14450, 14462, 14466, 14480, 14490,
%14502, 14510, 14516, 14520, 14526, 14532, 14538, 14540, 14552, 14586, 14592,
%14618, 14622, 14628, 14630, 14636, 14642, 14660, 14666, 14672, 14676, 14700,
%14718, 14726, 14736, 14742, 14748, 14750, 14760, 14768, 14790, 14792, 14798,
%14816, 14820, 14826, 14858, 14862, 14876, 14900, 14918, 14928, 14930, 14940,
%14952, 14958, 14966, 14982, 14996, 15002, 15006, 15012, 15026, 15036, 15048,
%15056, 15066, 15072, 15078, 15080, 15090, 15096, 15098, 15126, 15132, 15138,
%15150, 15162, 15182, 15206, 15210, 15212, 15216, 15246, 15248, 15258, 15272,
%15278, 15288, 15296, 15318, 15320, 15330, 15332, 15338, 15356, 15362, 15378,
%15402, 15408, 15420, 15440, 15446, 15450, 15468, 15476, 15488, 15492, 15500,
%15506, 15512, 15516, 15518, 15530, 15542, 15558, 15572, 15576, 15590, 15600,
%15612, 15618, 15626, 15632, 15638, 15642, 15650, 15660, 15672, 15678, 15686,
%15696, 15708, 15710, 15738, 15740, 15750, 15752, 15756, 15762, 15780, 15786,
%15792, 15806, 15818, 15828, 15840, 15842, 15846, 15852, 15860, 15866, 15882,
%15890, 15896, 15908, 15960, 15968, 15972, 15986, 15992, 16002, 16008, 16052,
%16058, 16070, 16086, 16092, 16100, 16112, 16116, 16122, 16130, 16148, 16158,
%16170, 16172, 16176, 16182, 16190, 16200, 16206, 16220, 16248, 16260, 16262,
%16268, 16280, 16286, 16322, 16326, 16338, 16356, 16358, 16380, 16386, 16388,
%16398, 16416, 16422, 16430, 16442, 16452, 16458, 16466, 16478, 16496, 16500,
%16506, 16508, 16512, 16518, 16532, 16542, 16556, 16562, 16566, 16568, 16580,
%16590, 16592, 16622, 16652, 16668, 16676, 16682, 16688, 16728, 16730, 16746,
%16760, 16770, 16772, 16776, 16788, 16800, 16806, 16808, 16812, 16818, 16826,
%16842, 16856, 16860, 16872, 16878, 16886, 16902, 16926, 16958, 16970, 16980,
%16982, 16988, 16998, 17012, 17030, 17036, 17040, 17042, 17060, 17102, 17108,
%17112, 17120, 17130, 17136, 17142, 17156, 17162, 17186, 17210, 17232, 17240,
%17246, 17250, 17268, 17270, 17276, 17292, 17306, 17310, 17322, 17346, 17348,
%17358, 17360, 17372, 17378, 17400, 17402, 17420, 17448, 17450, 17456, 17472,
%17478, 17490, 17492, 17516, 17526, 17532, 17540, 17556, 17558, 17562, 17576,
%17586, 17588, 17598, 17600, 17612, 17630, 17640, 17646, 17658, 17666, 17672,
%17676, 17690, 17696, 17700, 17702, 17712, 17718, 17730, 17768, 17796, 17808,
%17816, 17820, 17822, 17826, 17828, 17838, 17852, 17862, 17868, 17898, 17900,
%17910, 17912, 17936, 17940, 17948, 17960, 17966, 17982, 17988, 18008, 18018,
%18030, 18050, 18060, 18068, 18072, 18080, 18090, 18096, 18120, 18128, 18132,
%18138, 18152, 18156, 18170, 18186, 18198, 18216, 18228, 18246, 18270, 18272,
%18290, 18300, 18302, 18312, 18326, 18330, 18332, 18338, 18356, 18360, 18362,
%18366, 18368, 18372, 18380, 18390, 18402, 18410, 18416, 18426, 18432, 18438,
%18456, 18482, 18492, 18506, 18510, 18512, 18516, 18530, 18542, 18548, 18558,
%18576, 18582, 18590, 18600, 18608, 18612, 18626, 18632, 18636, 18638, 18642,
%18660, 18662, 18666, 18678, 18680, 18702, 18720, 18722, 18746, 18752, 18768,
%18780, 18806, 18810, 18816, 18818, 18822, 18830, 18836, 18842, 18852, 18858,
%18872, 18878, 18888, 18902, 18906, 18908, 18912, 18918, 18930, 18932, 18960]
? ## ***   last result computed in 21min, 1,383 ms. */