Does this sequence unexist?

 

Hello Math-Fun,

I wonder if the hereunder sequence will become stable at some point (and thus “exist”) or if it will be unstable forever (and thus “unexist”).

[1] we write down all the natural integers on a single row S, starting with 1;

S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,…

[2] we obey those rules:

  (a) start reading S from the very beginning of S;

  (b) if a single digit d stands between two digits having the same parity, raise d and add it to the digit immediately to its right (the term 195 becomes 114, for instance, and the 3-term succession 7, 8, 53 becomes the 2-term succession 7, 133); then go back to (a)

If I’m not wrong, the first 20 terms of S evolve like this (in yellow, the digit we raise – then add to the right):

S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  , 5, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  , 5,  , 9, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,15, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,1 ,14, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,1 ,1 , 50, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,1 ,  , 60, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  , 70, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,  7, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,  7,  2, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,  9, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,  9, 1 , 33, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,  9,   , 43, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,   ,   ,133, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,   ,   ,1 6, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,   ,   ,  7, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,   ,   ,  7, 1 , 55, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,   ,   ,  7,   , 65, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,   ,   ,   ,   ,135, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,   ,   ,   ,   , 18, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,   ,   ,   ,   ,  9, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,   ,   ,   ,   ,  9, 1 , 77, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,   ,   ,   ,   ,  9,   , 87, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,   ,   ,   ,   ,   ,   ,177, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,  ,  ,   ,   ,   ,   ,   ,   ,   ,114, 18, 19, 20, …

We see that a lot of terms have disappeared from S. But how will S evolve in the long run? Will it “stabilize” at some point (we would then have “for sure” a(1) = 1, a(2) = 14 and a(3) = 6, like above, for instance). Or is it possible that a new term, “far away”, “backtracks” the whole sequence and erases a(2) and a(3)?

Best,

É.

__________

Update, April 11th, 2022

Maximilian H. was quick to compute a few more terms (thank you, Maximilian, and thank you Hans H. for correcting the "rules" on top of this page):

S = 1, 14, 6, 79, 2, 2, 73, 2, 6, 7, 120, 99, 4, 4, 9, 122, 1, 124, 5, 106, 5, 128, 59, 6, 6, 154, 6, 116, 6, 138, 6, 1, 122, 7, 104, 7, 126, 7, 148, 79, 8, 8, 3, 102, 136, 8, 158, 89, ...

Below some "debugging output" from my program, concerning the terms up to a(16) = 122. (Thereafter there is again a lot of backtracking for a(17), but then it proceeds quite quickly to n=40-50.) 

At a(2)=2, digits [1,2,3]. At a(3)=4, digits [5,4,5]. At a(2)=5, digits [1,5,9]. At a(4)=7, digits [6,7,8]. At a(4)=15, digits [1,5,9]. At a(5)=14, digits [1,4,1]. At a(5)=1, digits [1,1,5]. At a(4)=1, digits [6,1,6]. At a(4)=70, digits [6,7,0]. At a(5)=11, digits [7,1,1]. At a(4)=7, digits [6,7,2]. At a(5)=12, digits [1,2,1]. At a(5)=1, digits [9,1,3]. At a(4)=9, digits [6,9,4]. At a(4)=133, digits [1,3,3]. At a(4)=16, digits [6,1,6]. At a(5)=14, digits [1,4,1]. At a(5)=1, digits [7,1,5]. At a(4)=7, digits [6,7,6]. At a(4)=135, digits [1,3,5]. At a(4)=18, digits [6,1,8]. At a(5)=16, digits [1,6,1]. At a(5)=1, digits [9,1,7]. At a(4)=9, digits [6,9,8]. At a(4)=177, digits [1,7,7]. At a(4)=114, digits [1,4,1]. At a(4)=11, digits [1,1,5]. At a(4)=1, digits [6,1,6]. At a(4)=78, digits [6,7,8]. At a(4)=15, digits [1,5,1]. At a(4)=1, digits [6,1,6]. At a(5)=20, digits [2,0,2]. At a(6)=21, digits [2,1,2]. At a(7)=32, digits [2,3,2]. At a(7)=5, digits [2,5,2]. At a(8)=24, digits [2,4,2]. At a(9)=65, digits [6,5,2]. At a(10)=76, digits [6,7,6]. At a(11)=27, digits [3,2,7]. At a(10)=13, digits [1,3,9]. At a(12)=28, digits [2,2,8]. At a(11)=12, digits [1,2,1]. At a(11)=1, digits [1,1,3]. At a(10)=1, digits [6,1,4]. At a(10)=50, digits [6,5,0]. At a(10)=5, digits [6,5,2]. At a(10)=79, digits [7,9,3]. At a(12)=31, digits [3,1,3]. At a(12)=3, digits [0,3,4]. At a(12)=72, digits [0,7,2]. At a(13)=33, digits [9,3,3]. At a(12)=9, digits [0,9,6]. At a(12)=15, digits [1,5,3]. At a(12)=1, digits [0,1,8]. At a(12)=94, digits [0,9,4]. At a(12)=13, digits [1,3,3]. At a(12)=1, digits [0,1,6]. At a(12)=75, digits [7,5,3]. At a(12)=7, digits [0,7,8]. At a(12)=156, digits [5,6,3]. At a(12)=15, digits [1,5,9]. At a(13)=147, digits [1,4,7]. At a(13)=111, digits [1,1,1]. At a(13)=12, digits [1,2,3]. At a(13)=1, digits [1,1,5]. At a(12)=1, digits [0,1,6]. At a(12)=78, digits [0,7,8]. At a(12)=15, digits [1,5,3]. At a(12)=1, digits [0,1,8]. At a(13)=40, digits [4,0,4]. At a(14)=41, digits [4,1,4]. At a(15)=52, digits [4,5,2]. At a(15)=7, digits [4,7,4]. At a(15)=113, digits [1,1,3]. At a(15)=14, digits [4,1,4]. At a(15)=5, digits [4,5,4]. At a(15)=94, digits [4,9,4]. At a(16)=45, digits [3,4,5]. At a(15)=13, digits [1,3,9]. At a(17)=46, digits [2,4,6]. At a(16)=12, digits [1,2,1]. At a(16)=1, digits [1,1,3]. At a(15)=1, digits [4,1,4]. At a(15)=50, digits [4,5,0]. At a(15)=5, digits [4,5,4]. At a(16)=48, digits [4,8,4]. At a(16)=4, digits [7,4,1]. At a(15)=97, digits [9,7,5]. At a(17)=50, digits [5,0,5]. At a(17)=5, digits [9,5,5]. At a(17)=101, digits [1,0,1]. At a(17)=11, digits [9,1,1]. At a(16)=1229, digits [2,9,2]. At a(17)=11, digits [1,1,5]. At a(17)=1, digits [2,1,6]. At a(17)=72, digits [2,7,2].  

____________________

April 16th update

Carole D. confirmed the first terms of Maximilian and sent to me a 2000-term b-file (and a graph). Merci Carole ! (to be submitted/incorporated soon to the OEIS):

S = 1, 14, 6, 79, 2, 2, 73, 2, 6, 7, 120, 99, 4, 4, 9, 122, 1, 124, 5, 106, 5, 128, 59, 6, 6, 154, 6, 116, 6, 138, 6, 1, 122, 7, 104, 7, 126, 7, 148, 79, 8, 8, 5140, 3, 124, 9, 146, 9, 168, 9, 100, 9, 104, 1308, 3, 102, 1326, 1128, 7, 104, 1344, 1146, 1348, 9, 164, 1366, 1568, 1104, 1380, 1182, 1384, 1586, 1788, 9, 100, 9, 104, 1128, 118, 4, 73, 2, 6, 13, 20, 17, 20, 912, 2, 136, 2, 310, 8, 13, 22, 15, 22, 118, 4, 134, 23, 10, 8, 112, 6, 13, 24, 116, 6, 138, 6, 1, 12, 45, 10, 65, 12, 8, 7, 1241, 1, 26, 114, 8, 136, 8, 158, 89, 1, 2, 27, 12, 67, 14, 8, 1, 100, 1, 120, 1, 160, 110, 2, 712, 2, 316, 2, 1300, 1506, 3, 108, 7, 122, 1524, 1326, 9, 124, 1142, 1344, 1546, 1160, 1362, 1564, 1766, 7, 104, 9, 382, 5, 384, 7, 386, 9, 388, 9, 122, 1146, 510, 8, 13, 40, 15, 40, 5, 14, 4, 134, 4, 518, 419, 4, 8, 7, 104, 9, 16, 4, 112, 43, 10, 8, 710, 4, 9, 1421, 1, 44, 114, 8, 136, 8, 11, 2, 4, 1, 14, 65, 12, 8, 1, 100, 1, 120, 910, 4, 912, 4, 318, 4, 1, 102, 1, 102, 1, 142, 792, 4, 336, 4, 7300, 1102, 1304, 5, 106, 5, 128, 1, 124, 1524, 7, 108, 1340, 1542, 1744, 9, 548, 9, 100, 9, 104, 1128, 1, 108, 5, 564, 7, 566, 9, 568, 9, 122, 1146, 1180, 5, 582, 7, 584, 9, 586, 9, 140, 1102, 1124, 1, 108, 150, 8, 13, 60, 5, 144, 132, 6, 1102, 114, 8, 9, 14, 89, 1, 2, 6, 910, 6, 9, 108, 11, 64, 110, 6, 712, 6, 914, 6, 1746, 1, 102, 110, 6, 972, 6, 714, 6, 1, 104, 1, 124, 110, 8, 510, 6, 712, 6, 9, 104, 7, 126, 7, 148, 3120, 1722, 9, 106, 9, 128, 1, 1229, 100, 9, 164, 3, 742, 5, 744, 7, 746, 9, 748, 1106, 1360, 5, 762, 7, 764, 9, 766, 9, 140, 1, 102, 1124, 9, 168, 7, 782, 9, 784, 9, 788, 3100, 1142, 1128, 1, 140, 5, 144, 1, 12, 81, 1, 2, 8, 7, 182, 5, 126, 1, 10, 8, 712, 8, 714, 8, 1764, 110, 8, 536, 8, 1, 148, 1126, 114, 8, 952, 8, 310, 8, 512, 8, 1, 1061, 106, 110, 8, 310, 8, 512, 8, 714, 8, 7, 10, 2, 9, 124, 9, 146, 9, 168, 9, 100, 9, 104, 3120, 3, 922, 5, 924, 7, 926, 9, 928, 9, 122, 9, 184, 5, 942, 7, 944, 9, 946, 9, 140, 1, 102, 9, 146, 1, 1461, 962, 9, 964, 9, 968, 3100, 9, 164, 9108, 1, 1481, 982, 9, 986, 3388, 3140, 910, 2, 9126, 7, 1001, 102, 9, 1005, 106, 9, 100, 1102, 9, 1023, 106, 5, 100, 9, 100, 1106, 9, 104, 7, 120, 1506, 9, 100, 9, 140, 1128, 9, 108, 9, 100, 1102, 5, 140, 1146, 9, 180, 1100, 7108, 1124, 1126, 3128, 1140, 7144, 3146, 5148, 5160, 1162, 3164, 5166, 7168, 9180, 3182, 5184, 7186, 9188, 7102, 1106, 1108, 5, 1201, 122, 1326, 1128, 3, 102, 1, 102, 1122, 1124, 1128, 7, 122, 9, 102, 1324, 1142, 1128, 9, 102, 9, 122, 1108, 1160, 1128, 7, 126, 5, 102, 1104, 9, 142, 1148, 1128, 7, 128, 9, 128, 7, 102, 7, 122, 3, 700, 1304, 1306, 3308, 1320, 1122, 1324, 3326, 5328, 5340, 1342, 3344, 5346, 7348, 7362, 5364, 7366, 9368, 7102, 1106, 1108, 3380, 5382, 7384, 9386, 7120, 1124, 1126, 3128, 9, 1401, 142, 1304, 1146, 1348, 5, 104, 1, 104, 1120, 1322, 1146, 1348, 1100, 7, 104, 9, 104, 7, 108, 1146, 1348, 1100, 1122, 9, 104, 7, 102, 9, 104, 1106, 1100, 3, 148, 1368, 7, 124, 9, 164, 7, 104, 1, 126, 5, 124, 1500, 1302, 1504, 3506, 5508, 5520, 1522, 3524, 5526, 7528, 9540, 3542, 5544, 7546, 9548, 7102, 1106, 1108, 3560, 5562, 7564, 9566, 7120, 1124, 1126, 3128, 5580, 7582, 9584, 7588, 1100, 1122, 1144, 3146, 5148, 1300, 1502, 1164, 1366, 1568, 7, 106, 1162, 1164, 1366, 1568, 1140, 9, 106, 5, 102, 1128, 1164, 3, 166, 5, 168, 1348, 9, 106, 9, 146, 9, 1661, 168, 1366, 9, 106, 9, 1467, 126, 11, 86, 11, 88, 11, 20, 1142, 3, 106, 7, 1269, 146, 1700, 1702, 3704, 5706, 7708, 9720, 3722, 5724, 7726, 9728, 7102, 1106, 1108, 3740, 5742, 7744, 9746, 1, 104, 1120, 1124, 1126, 3128, 5760, 7762, 9764, 1, 106, 1568, 1100, 1122, 1144, 3146, 5148, 7780, 9782, 1, 108, 1386, 1160, 1162, 3164, 5166, 7168, 1700, 1182, 1384, 1586, 1788, 9, 108, 3, 102, 1128, 1182, 3, 184, 5, 186, 7, 188, 9, 100, 1106, 1540, 5, 186, 7, 188, 9, 100, 11, 48, 1102, 1, 124, 3, 1085, 128, 9, 188, 9, 100, 11, 66, 1, 368, 11, 20, 1, 142, 3, 108, 5, 1287, 148, 1, 582, 11, 84, 1, 386, 1, 588, 116, 0, 3, 108, 5, 128, 7, 1489, 1689, 100, 3902, 5904, 7906, 9908, 7102, 9108, 3920, 5922, 7924, 9926, 3, 102, 1124, 1104, 7942, 9944, 3, 104, 3142, 1126, 9962, 3, 106, 9, 106, 3160, 1104, 5166, 7168, 9980, 3, 108, 7, 108, 9180, 3182, 5184, 7186, 9188, 37, 2, 2, 73, 2, 6, 13, 20, 17, 20, 912, 213, 20, 13, 20, 17, 20, 39, 2, 6, 13, 22, 15, 22, 118, 4, 11, 20, 13, 20, 17, 20, 57, 2011, 203, 120, 1104, 13, 24, 116, 6, 138, 6, 15, 20, 17, 20, 75, 2011, 2057, 2013, 205, 1241, 1, 26, 114, 8, 136, 8, 158, 89, 1, 209, 3, 2011, 2075, 2013, 2077, 2015, 207, 128, 35, 20, 592, 293, 2013, 2095, 2015, 2097, 2017, 209, 12, 2, 130, 8, 310, 2110, 2, 114, 2, 116, 2, 318, 2110, 2, 1, 14, 2, 112, 8, 112, 2, 134, 2, 336, 2110, 2138, 2112, 2, 1, 12, 2, 114, 6, 134, 8, 150, 2, 152, 2, 354, 2110, 2156, 2112, 2158, 2114, 2, 310, 2, 916, 8, 1, 12, 2170, 2, 372, 2110, 2174, 2112, 2176, 2114, 2178, 2116, 2, 518, 4, 158, 6, 178, 8, 116, 2, 910, 4112, 2194, 2114, 2196, 2116, 2198, 2118, 8, 13, 22, 15, 22, 59, 22, 13, 22, 15, 22, 37, 22, 5, 120, 1122, 13, 24, 116, 6, 99, 22, 11, 22, 15, 22, 55, 22, 77, 2211, 223, 1241, 1, 26, 114, 8, 136, 8, 11, 2, 4, 15, 227, 3, 229, 5, 2211, 2257, 2213, 225, 128, 1106, 110, 471, 22, 974, 475, 2213, 2277, 2215, 22, 1, 102, 1, 102, 1, 142, 39, 22, 992, 493, 2213, 2295, 2215, 2297, 2217, 229, 14, 2, 150, 63, 10, 8, 712, 2310, 2, 112, 2, 134, 2, 516, 2, 718, 2310, 2, 1, 12, 2, 132, 6, 712, 21, 10, 2330, 2, 152, 2, 534, 2, 736, 2310, 2338, 2312, 2, 1, 12, 8, 154, 6, 132, 27, 10, 2, 552, 2, 754, 2310, 2356, 2312, 2358, 2314, 2, 536, 4, 176, 6, 112, 2, 134, 2, 910, 4310, 2374, 2312, 2376, 2314, 2378, 2316, 2110, 2, 538, 4, 738, 6, 938, 8, 138, 2110, 2390, 2310, 2392, 2312, 2394, 2314, 2396, 2316, 2398, 2, 130, 8, 13, 24, 5, 10, 8, 51, 24, 13, 24, 35, 24, 57, 24, 7, 1241, 1, 26, 114, 8, 11029, 1, 245, 3, 247, 5, 249, 7, 2411, 243, 128, 1124, 110, 651, 24, 93, 24, 15, 2457, 2413, 24, 35, 24, 972, 673, 2411, 2475, 2413, 2477, 2415, 24, 57, 24, 112, 893, 2413, 2495, 2415, 2497, 2417, 249, 16, 2, 130, 45, 10, 65, 12, 8, 150, 2, 152, 2, 714, 2, 916, 2, 910, 2, 1, 14, 67, 10, 8, 150, 27, 10, 2, 732, 2, 934, 2, 910, 2538, 2512, 2, 554, 4, 954, 8, 152, 2, 910, 4, 910, 2556, 2512, 2558, 2514, 2110, 2, 556, 4, 756, 6, 956, 8, 138, 2110, 2570, 2, 910, 2574, 2512, 2576, 2514, 2578, 2516, 2130, 2, 758, 4, 958, 6, 156, 2110, 2138, 2112, 2590, 2510, 2592, 2512, 2594, 2514, 2596, 2516, 2598, 2, 172, 8, 1, 12, 81, 1, 263, 3, 265, 5, 267, 7, 269, 128, 1142, 110, 831, 26, 73, 26, 95, 26, 1164, 39, 26, 91, 26, 13, 2655, 2611, 2657, 2613, 26, 1, 126, 99, 26, 310, 811, 2675, 2613, 2677, 2615, 26, 11281, 106, 57, 26, 352, 893, 2613, 2695, 2615, 2697, 2617, 269, 18, 271, 2, 27, 12, 67, 14, 8, 11209, 10, 29, 12, 2, 112, 2716, 2, 7, 18, 491, 4, 29, 12, 8, 1122, 9, 100, 910, 4, 136, 2710, 2738, 2712, 2110, 2, 574, 4, 774, 6, 974, 8, 138, 2110, 2750, 2, 154, 2710, 2756, 2712, 2758, 2714, 2130, 2, 776, 4, 976, 6, 156, 2110, 2138, 2112, 2770, 2, 312, 2710, 2774, 2712, 2776, 2714, 2778, 2716, 2150, 2, 978, 4, 174, 2110, 2156, 2112, 2158, 2114, 2790, 2710, 2792, 2712, 2794, 2714, 2796, 2716, 2798, 2, 1160, 11, 2815, 28, 97, 28, 1182, 1, 100, 13, 28, 13, 28, 1, 106, 99, 28, 11, 2853, 28, 11, 2811, 2857, 281, 104, 17, 28, 11, 2811, 2875, 2813, 2877, 2815, 28, 1168, 1, 108, 9, 10091, 2811, 2893, 2813, 2895, 2815, 2897, 2817, 28, 110, 2, 712, 2, 310, 8, 910, 2910, 2, 316, 21, 18, 2910, 2110, 2, 592, 4, 792, 6, 992, 8, 912, 2, 334, 21, 36, 2910, 2938, 2912, 2130, 2, 794, 4, 994, 6, 9, 140112, 2950, 21, 32, 21, 54, 2910, 2956, 2912, 2958, 2914, 2150, 2, 996, 4, 996, 8112, 2158, 2114, 2970, 217, 2, 2910, 2974, 2912, 2976, 2914, 2978, 2916, 2170, 2, 998, 6112, 2176, 2114, 2178, 2116, 2990, 2910, 2992, 2912, 2994, 2914, 2996, 2916, 2998, 2, 3, 3001, 302, 1506, 3, 108, 3, 120, 1, 1201, 100, 9, 3021, 304, 1106, 1308, 7, 302, 9, 1203, 100, 1104, 1106, 1308, 9, 120, 1, 100, 7, 1405, 100, 1506, 1308, 7, 306, 1, 1069, 100, 5, 120, 1104, 9, 1607, 100, 7, 308, 9, 308, 71089, 120, 7, 140, 1144, 1106, 5100, 1300, 1304, 1306, 5108, 1320, 1122, 1324, 5126, 7128, 7140, 1342, 5144, 7146, 9148, 9162, 7164, 9166, 1100, 5180, 7182, 9184, 1388, 3104, 1126, 5108, 9, 3201, 322, 1124, 1326, 7, 320, 1120, 1124, 1326, 1528, 9, 122, 9, 1223, 102, 1324, 1326, 1528, 1100, 9, 102, 9, 122, 1106, 1, 1025, 128, 3, 328, 1, 108, 1, 1089, 120, 9, 122, 1124, 1106, 1128, 7, 328, 7, 328, 3, 122, 1102, 1100, 1302, 1504, 5306, 7308, 7320, 1522, 5324, 7326, 9328, 5342, 7344, 9346, 1100, 1560, 7362, 9364, 1568, 1104, 1126, 5108, 7380, 9382, 1586, 1122, 1144, 5126, 7128, 1300, 1142, 1344, 1546, 9, 124, 1342, 1344, 1546, 1748, 9, 102, 5, 104, 1544, 3, 346, 5, 348, 1348, 7, 104, 1104, 1106, 1128, 1546, 5, 348, 1366, 7146, 9, 124, 9, 1647, 104, 1382, 1104, 11, 88, 11, 20, 9, 1249, 1041, 104, 1700, 1702, 5504, 7506, 9508, 5522, 7524, 9526, 1100, 1740, 7542, 9544, 1748, 1104, 1126, 5108, 7560, 9562, 1766, 1122, 1144, 5126, 7128, 9580, 1784, 1140, 1162, 5144, 7146, 9148, 1160, 1362, 1564, 1766, 9, 102, 5, 106, 1362, 3, 364, 5, 366, 7, 368, 9, 100, 9, 122, 1146, 1128, 1564, 5, 366, 7, 368, 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