Same
parity jumps
Hello SeqFans,
The sequence J must be read, digit by digit, from left to right; any
digit “d” of J says: “Jump to the right over “d”
digit and you’ll land on a digit with the same parity as me”.
J was build starting with a(1) = 1 and was
always extended with the smallest unused integer not leading to a
contradiction.
J = 1, ...
This first integer
constrains the future of J – as the digit “1”
asks for a jump of size “1” to land on an odd digit. The landing spot is marked
here with a lower “o” (for “odd”):
J = 1, . , . ,
...
|______o
As we want to extend J with the smallest unused integer so far not leading to a
contradiction, we will fill the first “hole” with “2”:
J = 1, 2 , . ,
...
o
But this “2”
constrains the fure of J too. We
thus mark the next landing spot with an upper “e” (“even”):
___________
| e
J = 1, 2 , . , . , . ,
...
o
We see, after a quick
check, that “3” fits in the next “hole”. “3” puts a
“o-mark” 3 steps to its right:
e
J = 1, 2 , 3 , . , . , . , . ,...
o o
Again, a quick check
allows us to write “4” in the next “hole”. “4” puts a
“e-mark” 4 steps to its right:
e e
J = 1, 2 , 3 , 4 , . , . , . , . , . ,...
o o
The next “hole” can’t
be filled with an odd digit, as indicated by the “e-mark”. But “6” fits:
e
e
e
J = 1, 2 , 3 , 4 , 6 , . , . , . , . , . , . , . ,
...
o o
Does “5” have its
place in the next “hole”? Let’s try:
e e e
J = 1, 2 , 3 , 4 , 6 , 5 , . , . , . , . , . , . , . , ...
o o
No, this doesn’t work
as “5” forces us to “o-mark” a digit 5 steps to its right that is already
“e-marked”:
e
e
e
J = 1, 2 , 3 , 4 , 6 , 5 , . , . , . , . , . , . , . , ...
o o o
We then discard “5”
and try “7” instead, the smallest unused integer so far; which is ok:
e
e
e
J = 1, 2 , 3 , 4 , 6 , 7 , . , . , . , . , . , . , . , . ,
...
o o
o
The next digit must
be odd, according to the mark; does “5”, the smallest odd integer not used so
far, fit?
e e e
J = 1, 2 , 3 , 4 , 6 , 7 , 5 , . , . , . , . , . , . , . , ...
o o o o
Yes, the “o-mark” doesn’t
produce any conflict. We proceed with “8”, the
smallest available integer:
e
e
e e
J = 1, 2 , 3 , 4 , 6 , 7 , 5 , 8 , . , . , . , . , . , . , . , . , . , ...
o o o o
The next hole must be
occupied by an even digit; as the single-digit integers 2, 4, 6 and 8 are
already used, we must find the smallest 2-digit integer that fits. This is 20:
e e e
e e
J = 1, 2 , 3 , 4 , 6 , 7 , 5 , 8 , 20 , . , . , . , . , . , . , . , ...
o o o o
“20” fits because both
digits “2” and “0” fit: “2” puts a second “e-mark” on a previous “e-mark” (in
yellow here); and “0” forces us to put an “e-mark” (in gray) immediately right
to “0” (this is a jump of size zero).
The next integer will
probably be a 2-digit one again; but we cannot put “2” under the gray mark, as
this would produce a conflict with the second “o-mark” to the right; the
2-digit integer we are looking for is 42:
e e ee e e
e
J = 1, 2 , 3 , 4 , 6 , 7 , 5 , 8 , 20 , 42 , . , . , . , . , . , ...
o o o o
“9”, the smallest
unused odd integer is available for the next “hole”; the “o-mark” produced is
at the end:
e
e ee
e e e
J = 1, 2 , 3 , 4 , 6 , 7 , 5 , 8 , 20 , 42 , 9 , . , . , . , . , . , . , . , . , . , . , ...
o o o o o
Then next integer
will have more than one digit as 1, 3, 5, 7 and 9 are already used; the first
digit of this integer caznnot be “1” – as “1”
produces a conflict with the middle “e-mark” to the right. Let’s try “30”:
e e ee e e e
J = 1, 2 , 3 , 4 , 6 , 7 , 5 , 8 , 20 , 42 , 9 , 30 , . , . , . , . , . , . , . , . , ...
o o o o
o o
“30” is ok – as “3”
puts an “0-mark” on a free spot (in gray, above) and
“0” puts an “e-mark” on a previous one (in yellow, above). What would be the
next integer? Yes, “22” is the one – as “smallest unused integer composed of
two even digits”:
e
e ee
e ee
e e
J = 1, 2 , 3 , 4 , 6 , 7 , 5 , 8 , 20 , 42 , 9 , 30 , 22 , . , . , . , . , . , . , ...
o o o o o o
For similar
conflicting reasons, the next “holes” cannot be filled with an integer cannot
starting with “1”; the smallest available one is “34”:
e e ee e ee e e e
J = 1, 2 , 3 , 4 , 6 , 7 , 5 , 8 , 20 , 42 , 9 , 30 , 22 , 34 , . , . , . , . , . ,...
o o o o
o o o
.... and so on:
e e ee e ee e e
e e
J = 1, 2 , 3 , 4 , 6 , 7 , 5 , 8 , 20 , 42 , 9 , 30 , 22 , 34 , 41 , . , . , . , . , . , ...
o o o o
o o o
e e ee e ee e e
e e
J = 1, 2 , 3 , 4 , 6 , 7 , 5 , 8 , 20 , 42 , 9 , 30 , 22 , 34 , 41 , 33 , . , . , . , . , ...
o o o o
o oo
o o
e e ee e ee e e
ee e e
J = 1, 2 , 3 , 4 , 6 , 7 , 5 , 8 , 20 , 42 , 9 , 30 , 22 , 34 , 41 , 33 , 44 , . , . , . , . , . , ...
o o o o
o oo
o o
e e ee e ee e e
ee e e
J = 1, 2 , 3 , 4 , 6 , 7 , 5 , 8 , 20 , 42 , 9 , 30 , 22 , 34 , 41 , 33 , 44 , 13 , . , . , . , . , ...
o o o o
o oo
oo o o
e e ee e ee e e
ee e e
J = 1, 2 , 3 , 4 , 6 , 7 , 5 , 8 , 20 , 42 , 9 , 30 , 22 , 34 , 41 , 33 , 44 , 13 , 36 , . , . , . , ...
o o o o
o oo
oo o o
o
If I’m not wrong, the
first 19 terms of J are:
J = 1, 2, 3, 4, 6, 7, 5, 8, 20, 42, 9, 30, 22, 34, 41, 33, 44, 13, 36, ...
Any taker to check, extend and publish this insanity?
;-D
Best,
É.
__________
[Lars Blomberg]:
The sequence J seems to be finite (without using backtracking).
After 4016 terns the
pattern to be matched by the next number is (best viewed in a fixed font):
ExOOxOxOxOxx
2--e
4----e
6------e
8--------e
where E requires an even digit, O requires an
odd digit, and x don’t care.
As illustrated, all
possible even numbers will require an even number 2,4,6,8 positions away, but
all these positions already requires an odd number.
If the phrase
"not leading to a contradiction" is to be interpreted as "backtracking
must be used", then there is more work ahead.
The 4016 values are:
J = 1, 2, 3, 4, 6, 7, 5, 8, 20, 42, 9, 30, 22, 34, 41, 33, 44, 13, 36, 23, 12,
31, 25, 14, 11, 35, 24, 16, 37, 26, 38, 45, 39, 46, 73, 60, 47, 27, 18, 15, 17,
19, 51, 49, 29, 50, 81, 53, 55, 57, 56, 71, 59, 75, 28, 58, 61, 77, 52, 64, 48,
93, 40, 63, 66, 67, 70, 62, 68, 69, 72, 78, 80, 83, 79, 95, 84, 82, 91, 85, 90,
88, 89, 74, 86, 94, 423, 92, 412, 96, 402, 97, 406, 99, 413, 304, 113, 123, 125,
127, 129, 141, 131, 411, 312, 314, 115, 145, 133, 415, 300, 231, 233, 417, 302,
230, 235, 223, 425, 306, 111, 135, 225, 227, 229, 200, 234, 419, 308, 117, 119,
318, 137, 147, 330, 237, 239, 241, 236, 427, 340, 238, 251, 250, 252, 256, 255,
253, 451, 316, 139, 149, 202, 404, 502, 342, 334, 257, 206, 258, 259, 270, 272,
408, 336, 151, 274, 273, 422, 344, 153, 441, 338, 271, 275, 604, 155, 161, 157,
208, 277, 278, 414, 512, 346, 159, 204, 279, 424, 504, 163, 167, 348, 290, 291,
294, 245, 247, 249, 240, 292, 416, 350, 293, 418, 356, 171, 296, 426, 360, 295,
220, 261, 297, 222, 244, 299, 224, 226, 429, 362, 450, 442, 352, 452, 358, 173,
175, 364, 177, 366, 179, 370, 453, 368, 191, 372, 374, 193, 181, 195, 183, 169,
185, 228, 447, 380, 470, 456, 382, 378, 457, 386, 390, 455, 246, 459, 242, 458,
444, 550, 446, 392, 472, 260, 445, 384, 473, 428, 388, 197, 248, 264, 475, 266,
449, 394, 474, 506, 189, 199, 280, 606, 715, 341, 471, 478, 396, 311, 530, 461,
514, 508, 347, 351, 490, 492, 284, 263, 463, 522, 524, 523, 345, 331, 477, 262,
448, 534, 467, 500, 462, 516, 702, 520, 469, 518, 526, 349, 538, 479, 528, 562,
552, 536, 315, 333, 491, 556, 317, 335, 611, 513, 361, 313, 558, 319, 353, 494,
572, 564, 515, 566, 355, 570, 493, 574, 517, 363, 357, 578, 337, 359, 590, 495,
584, 519, 525, 367, 371, 592, 496, 700, 267, 269, 268, 612, 568, 582, 586, 704,
527, 481, 594, 497, 580, 613, 533, 369, 373, 596, 339, 375, 615, 529, 381, 377,
499, 588, 379, 553, 706, 391, 393, 614, 535, 383, 395, 537, 385, 397, 539, 389,
399, 555, 561, 511, 712, 560, 483, 708, 557, 485, 714, 559, 489, 718, 563, 567,
716, 730, 631, 617, 569, 464, 750, 608, 573, 466, 722, 720, 281, 619, 575, 581,
531, 577, 583, 571, 579, 585, 589, 593, 723, 724, 725, 283, 623, 726, 727, 285,
289, 633, 625, 728, 923, 729, 740, 635, 627, 745, 286, 637, 595, 641, 597, 823,
741, 551, 639, 599, 482, 734, 713, 747, 591, 671, 717, 749, 731, 673, 629, 742,
780, 645, 733, 647, 735, 649, 675, 288, 661, 719, 744, 663, 667, 746, 600, 677,
282, 468, 912, 748, 630, 679, 400, 484, 736, 785, 669, 683, 486, 782, 784, 685,
689, 783, 624, 789, 781, 693, 825, 786, 681, 695, 620, 827, 829, 440, 634, 697,
788, 640, 699, 420, 626, 845, 900, 831, 691, 636, 847, 841, 638, 833, 849, 738,
837, 811, 752, 670, 813, 902, 756, 616, 737, 861, 815, 758, 839, 2512, 904, 739,
941, 751, 618, 913, 906, 770, 674, 817, 908, 930, 819, 772, 678, 853, 942, 778,
660, 855, 940, 835, 851, 755, 690, 857, 800, 859, 672, 692, 488, 920, 863, 602,
774, 628, 867, 922, 460, 694, 696, 644, 869, 2250, 646, 757, 806, 891, 759, 648,
893, 622, 924, 883, 642, 790, 680, 885, 889, 925, 808, 881, 771, 830, 4253, 662,
792, 684, 773, 927, 929, 945, 753, 895, 711, 775, 897, 777, 779, 6111, 791, 899,
795, 793, 6115, 794, 2330, 2312, 796, 686, 797, 2230, 4113, 926, 928, 480, 812,
914, 946, 802, 834, 2350, 814, 799, 688, 2234, 2334, 2336, 2314, 916, 947, 836,
2316, 918, 931, 2514, 944, 948, 840, 850, 838, 2318, 934, 949, 960, 816, 936, 935,
2338, 911, 915, 938, 917, 919, 950, 818, 937, 951, 852, 856, 858, 890, 892, 804,
2252, 894, 896, 820, 2256, 2302, 952, 842, 956, 2304, 958, 961, 953, 972, 970, 4115,
963, 955, 966, 957, 978, 2306, 939, 967, 860, 4123, 962, 968, 846, 974, 2300, 4117,
969, 959, 990, 4119, 1411, 994, 933, 1413, 992, 996, 848, 971, 2516, 1251, 2308,
973, 822, 964, 975, 866, 977, 3304, 979, 1230, 6117, 991, 2352, 3123, 1231, 2356,
995, 993, 8111, 997, 3125, 1415, 3141, 999, 2000, 664, 1133, 4233, 4235, 2236, 2358,
2342, 5300, 2370, 2340, 2372, 2344, 1330, 2374, 1131, 2378, 1111, 1135, 2238, 2390,
2346, 2348, 3302, 5123, 4237, 2258, 666, 1153, 668, 1137, 2270, 682, 5025, 2272,
2360, 2518, 1233, 4133, 4239, 2274, 824, 1253, 844, 1350, 2362, 3127, 1234, 4135,
2278, 2364, 1139, 2290, 826, 1250, 2366, 1113, 3023, 1235, 2292, 2368, 1115, 1236,
2392, 2380, 2382, 3306, 1312, 3129, 1237, 2294, 4125, 864, 1155, 868, 1117, 5000,
4137, 1238, 4139, 1239, 2296, 2386, 2384, 5304, 2394, 2388, 2396, 1352, 2502, 3025,
1252, 2504, 1151, 2506, 1119, 3002, 3004, 1157, 862, 2508, 3027, 1255, 884, 1159,
2002, 3006, 1171, 2500, 4153, 882, 3145, 3008, 1173, 828, 1271, 2520, 4255, 880,
2712, 3042, 3308, 1175, 886, 1257, 888, 2702, 5004, 2530, 4155, 1412, 3147, 1256,
4023, 3029, 1258, 2004, 1177, 2006, 1179, 2008, 1191, 1193, 4025, 1414, 5125, 2412,
3149, 1270, 2040, 2534, 1195, 2042, 2522, 3041, 1314, 1197, 2020, 4027, 1259, 4029,
1272, 2560, 4157, 1416, 3045, 3044, 1334, 2536, 4159, 2022, 3046, 1316, 3161, 3163,
1273, 4045, 1274, 2524, 4257, 2024, 1275, 2044, 1336, 2550, 4047, 1278, 4049, 1290,
2046, 1318, 3167, 1199, 4083, 1417, 3362, 3169, 1277, 2060, 4173, 1279, 2538, 1291,
2526, 4063, 3047, 1292, 4067, 1418, 3049, 1294, 2048, 2528, 1293, 4069, 2026, 1295,
2562, 3183, 1297, 2028, 1419, 5006, 2414, 5127, 2416, 3061, 3185, 1296, 2552, 3063,
1299, 2080, 2062, 3502, 3067, 1450, 4085, 1451, 2564, 1453, 4089, 1452, 2064, 1530,
4259, 2082, 3048, 1338, 1331, 2556, 4127, 3022, 3069, 1455, 2066, 1512, 3081, 1311,
1356, 1313, 3181, 1315, 1358, 1317, 1333, 4175, 1611, 1335, 2558, 1319, 1337, 2570,
4129, 1456, 2068, 3189, 1457, 2084, 1339, 2572, 3083, 1351, 1372, 3341, 1370, 2566,
1459, 2086, 1355, 2568, 1513, 1471, 2580, 4177, 1614, 1353, 4145, 1458, 2582, 5027,
2418, 3085, 1357, 2574, 1359, 2578, 1371, 1373, 4179, 1613, 1375, 2584, 1377, 2586,
1379, 2588, 1391, 1378, 2594, 1393, 4147, 1472, 3089, 1374, 1390, 2590, 4149, 1474,
5008, 2592, 4163, 4413, 3423, 3425, 3062, 3504, 1473, 4167, 1470, 4223, 4273, 4225,
2450, 2704, 1392, 2700, 2088, 1394, 1396, 2596, 3345, 3342, 3344, 1534, 4193, 4227,
2402, 3347, 1514, 1395, 2706, 1397, 3361, 1515, 1475, 2708, 1399, 1531, 6119, 1516,
1477, 2720, 6231, 2714, 1478, 2724, 1479, 2726, 1490, 2722, 2404, 5129, 2452, 2406,
3346, 3348, 3364, 1533, 4275, 2200, 2716, 1491, 2728, 1492, 5141, 2718, 1493, 4169,
2408, 3064, 1535, 6235, 2730, 2734, 1536, 4195, 2202, 2742, 3066, 1517, 3427, 3429,
3441, 3366, 1518, 3445, 5040, 2736, 1494, 2740, 2442, 3368, 1519, 1495, 2206, 2744,
5044, 2738, 2470, 2746, 2456, 2748, 3068, 1537, 4277, 4229, 4279, 2204, 2750, 2752,
3349, 1538, 1497, 2780, 6041, 1550, 4183, 1499, 2208, 2444, 5306, 2756, 2446, 3382,
3367, 1552, 3447, 3024, 1631, 2758, 2448, 5308, 2770, 2240, 2772, 2244, 2774, 2246,
2778, 2248, 2790, 2242, 2782, 3082, 3384, 1730, 2458, 2784, 1496, 2786, 2462, 3506,
1615, 5041, 2792, 2260, 2788, 1612, 5340, 2794, 1539, 4197, 1811, 1511, 3363, 1553,
1617, 1551, 4185, 1616, 1556, 4189, 3026, 1618, 5145, 2472, 2900, 2474, 4245, 2478,
2904, 1555, 6045, 1558, 1571, 1557, 4199, 1813, 1559, 3381, 1711, 1570, 4513, 1619,
1572, 6047, 1574, 1573, 4293, 4295, 2466, 3508, 3449, 5020, 2490, 2902, 2422, 3461,
3522, 3463, 3467, 3028, 1633, 1575, 6049, 1578, 1577, 1579, 4297, 2492, 3369, 1592,
3469, 3523, 1635, 1590, 4515, 1637, 1591, 4517, 1639, 1593, 6061, 1594, 1831, 2796,
3086, 3385, 3386, 1712, 3084, 1731, 2912, 3383, 1715, 1596, 1595, 3389, 1714, 1630,
2930, 2494, 4247, 2424, 5023, 4299, 2220, 2464, 5147, 2496, 3481, 3388, 1716, 1670,
2906, 2612, 5029, 2614, 1597, 4519, 1671, 1599, 4533, 1673, 1733, 6131, 1718, 1634,
1734, 2630, 2934, 2634, 4453, 4423, 3483, 3485, 3088, 1736, 1672, 2908, 2616, 1675,
2264, 2936, 2618, 5045, 2636, 2950, 2426, 3489, 3402, 3404, 5149, 2638, 1636, 2952,
2428, 3623, 1677, 2224, 4455, 2468, 3524, 1679, 2226, 2670, 2920, 2672, 4249, 2674,
1638, 2938, 2678, 4263, 4457, 2482, 3625, 1674, 2924, 2690, 4267, 2484, 5047, 2692,
4269, 2486, 3406, 3526, 3627, 5024, 4459, 2488, 3408, 5344, 2956, 2602, 5049, 2694,
1735, 2914, 1737, 8113, 1713, 1691, 1738, 2696, 1750, 2604, 1739, 2812, 3561, 3525,
1693, 1751, 2916, 1717, 3563, 1719, 1678, 1770, 2958, 2918, 1695, 6067, 2922, 3629,
1697, 2262, 4523, 1699, 1752, 2606, 1753, 6069, 1756, 1692, 5161, 2972, 3604, 1755,
2608, 1771, 2940, 2970, 4283, 4415, 3442, 3528, 1815, 1690, 2926, 2622, 5061, 2974,
1694, 4473, 4623, 1833, 4417, 3422, 3641, 1758, 2642, 5346, 2978, 2228, 4475, 2266,
2990, 2222, 4425, 3444, 5348, 2992, 2268, 4419, 5026, 2814, 7123, 4427, 3424, 5063,
4477, 2280, 4479, 2284, 2830, 2994, 2282, 4429, 3426, 3446, 3562, 3527, 1817, 1757,
3567, 1759, 1819, 1772, 2944, 1774, 6081, 2996, 1778, 3569, 1773, 6085, 1790, 2942,
2928, 1835, 1775, 2946, 1792, 3581, 1777, 1696, 1779, 2644, 1794, 2948, 2962, 5067,
4493, 3823, 1851, 3529, 3645, 1796, 2960, 2964, 1837, 4495, 3841, 1912, 3428, 3647,
1830, 4497, 2286, 4445, 3448, 3564, 1793, 6089, 1914, 1834, 4553, 4447, 3462, 3583,
1839, 1812, 3464, 5163, 4499, 2288, 2646, 1950, 2624, 1853, 4449, 3482, 3466, 3566,
3649, 5028, 2816, 1791, 2966, 1795, 3845, 1916, 3568, 3585, 1855, 2968, 3582, 5069,
2818, 1814, 7125, 2648, 1930, 2834, 4555, 6441, 3584, 1797, 2400, 4525, 1857, 1799,
3589, 1911, 1918, 1913, 1859, 4483, 3661, 1934, 2836, 4557, 3663, 1893, 4285, 2662,
5500, 4613, 1891, 4500, 4463, 3667, 1836, 4615, 5046, 4512, 3669, 1838, 2890, 4502,
4467, 3468, 3683, 1895, 2440, 4504, 1897, 2420, 4469, 3484, 5048, 4514, 1899, 2480,
2664, 1936, 2850, 4485, 3486, 3702, 3488, 3704, 1850, 4506, 3681, 5167, 2838, 3411,
5169, 2852, 2666, 7127, 2626, 7023, 4489, 3602, 5060, 4516, 3413, 3685, 1852, 4508,
3689, 1856, 2668, 5183, 4635, 2856, 4518, 3825, 1858, 4522, 5081, 4712, 3606, 1951,
4524, 5083, 4617, 1890, 4289, 2628, 1892, 4520, 4625, 1894, 4526, 4627, 5064, 4535,
6237, 4530, 4619, 1896, 2460, 4527, 3415, 3741, 1938, 1915, 1931, 4537, 3417, 3723,
3419, 3586, 1917, 3588, 1919, 1952, 8061, 1933, 3451, 3725, 1816, 1953, 3727, 3453,
3729, 1818, 1970, 4528, 4633, 4637, 2858, 4529, 5085, 2892, 3706, 3608, 5181, 4730,
2894, 1955, 2682, 5185, 2896, 1956, 2684, 5089, 4230, 6230, 4534, 4639, 4234, 6234,
4536, 4673, 4629, 4236, 6250, 4562, 3827, 3412, 3745, 1958, 1935, 1937, 4539, 3455,
3642, 5360, 4538, 3471, 5189, 4238, 6236, 4550, 4645, 5066, 4552, 3829, 3414, 5068,
4570, 4647, 4250, 4649, 5080, 6135, 1972, 3708, 1939, 1957, 8063, 1959, 2686, 1971,
4560, 4675, 2600, 4556, 4663, 5223, 4677, 2620, 4679, 2640, 6238, 4572, 4667, 4252,
4669, 5084, 6239, 4558, 3473, 5341, 4574, 4683, 4695, 2800, 4559, 3847, 1974, 4563,
4693, 4823, 4685, 5086, 4714, 5088, 4715, 5200, 4573, 3611, 1973, 4567, 3457, 3861,
1975, 2660, 4575, 6241, 4578, 3613, 1977, 2680, 4697, 2802, 4569, 3849, 3416, 3742,
3744, 1978, 4564, 4699, 2806, 2688, 5345, 6330, 4590, 4813, 3459, 3622, 5204, 4577,
4689, 4835, 6252, 4566, 3475, 3644, 1990, 2808, 1979, 5206, 6151, 3722, 3646, 1992,
2820, 4815, 3648, 5364, 4579, 4817, 3418, 3747, 1994, 4583, 4819, 3452, 3662, 5504,
4833, 4853, 3863, 3749, 3682, 5347, 4592, 3867, 1993, 3869, 1995, 3802, 3781, 3746,
1996, 3726, 3881, 3724, 5208, 4593, 4825, 2804, 7129, 2822, 3664, 5506, 4855, 2842,
3728, 3666, 1997, 2826, 3477, 3624, 5231, 4594, 4827, 2824, 7025, 2844, 7300, 4568,
3479, 5220, 6251, 4582, 3885, 3312, 3748, 3314, 1991, 4580, 4829, 3456, 3668, 5508,
4837, 4256, 4845, 3684, 5349, 4596, 3491, 3782, 3686, 7302, 4584, 5225, 6256, 4586,
3889, 3626, 7000, 4585, 3495, 3786, 1999, 3788, 3111, 5330, 4595, 3493, 3783, 3115,
3316, 3113, 3785, 3117, 3318, 3119, 5131, 6137, 3334, 5133, 4597, 3497, 3789, 3131,
3336, 3151, 3784, 5135, 6312, 3902, 3628, 5227, 4258, 4839, 7250, 2846, 3352, 3904,
5137, 4599, 3499, 3806, 3153, 3923, 3615, 5139, 4713, 3617, 5151, 4717, 3458, 3925,
5230, 4719, 3472, 3906, 3155, 3883, 3157, 3688, 5171, 4734, 6255, 6302, 3908, 3133,
5153, 4733, 3619, 5155, 6139, 3338, 3135, 5157, 4716, 3671, 5361, 4718, 3474, 5363,
4735, 3478, 3924, 5233, 4737, 3492, 3927, 3494, 5229, 4412, 3804, 7141, 4588, 3631,
5334, 4736, 6257, 4702, 5241, 4738, 3496, 7145, 2848, 3372, 5366, 4750, 2862, 3922,
3808, 3171, 5367, 4739, 3633, 5159, 4752, 3842, 3926, 3822, 7027, 2828, 3673, 5245,
6258, 4704, 5234, 4753, 6411, 3928, 3612, 5247, 4270, 4847, 3614, 5249, 4272, 2840,
4756, 2864, 7147, 2866, 3159, 3824, 7002, 4589, 3635, 5236, 4755, 2868, 3173, 5261,
4757, 2882, 3929, 3826, 3675, 5368, 4770, 2860, 4758, 2884, 7149, 2886, 3175, 3944,
5336, 4759, 2888, 3177, 5380, 4775, 2880, 4772, 3844, 7350, 4706, 3616, 7161, 4708,
3618, 5173, 4773, 6259, 4774, 5235, 6155, 3356, 3179, 3828, 3672, 5369, 4777, 3634,
5175, 6157, 3358, 3137, 5177, 4779, 3637, 5179, 4793, 3811, 3191, 3941, 3374, 5191,
4778, 3636, 7151, 4722, 3846, 3378, 3945, 5238, 4795, 5237, 4792, 5263, 4797, 3812,
3947, 3862, 3949, 3882, 3961, 3962, 5267, 4857, 3677, 5269, 4799, 3813, 3193, 3963,
3139, 3639, 5193, 6159, 3392, 3942, 3964, 5195, 6271, 4724, 5239, 4790, 6000, 4726,
3674, 5381, 4794, 5240, 4796, 3815, 3946, 3966, 3967, 5283, 4859, 3678, 5244, 4930,
4274, 4849, 4278, 6004, 4934, 4290, 4863, 3679, 5224, 6270, 4700, 6272, 4720, 6274,
4728, 6275, 6300, 4912, 3864, 7029, 4002, 3848, 3394, 5383, 4915, 3638, 5197, 4292,
4867, 3692, 5281, 4914, 5226, 4893, 4869, 3884, 7006, 4742, 3866, 3195, 3868, 3197,
5228, 4895, 7008, 4723, 5251, 4913, 3691, 5199, 4416, 3886, 3948, 3888, 9025, 6006,
4916, 7020, 4883, 3695, 5246, 4918, 5260, 4897, 4000, 4885, 3694, 5386, 4917, 5264,
4899, 4006, 6002, 3968, 3199, 5253, 6171, 3396, 3311, 3969, 3512, 5285, 6175, 3514,
5331, 4919, 3693, 5255, 6177, 3516, 3313, 5385, 3315, 3518, 3317, 5333, 4933, 3697,
5257, 4935, 3699, 5335, 6179, 3534, 5259, 4936, 3696, 7163, 4725, 3814, 7153, 4727,
3816, 3319, 5384, 5337, 4938, 3817, 7061, 4729, 3818, 3371, 5388, 4937, 4294, 4889,
4004, 5248, 4970, 4008, 6277, 4020, 6279, 4024, 5250, 4939, 3819, 3351, 5389, 3331,
3536, 3353, 5523, 3831, 3355, 5561, 3513, 3833, 3357, 5524, 5271, 4950, 4414, 5289,
4296, 6008, 4744, 5256, 4952, 5604, 5273, 4953, 3835, 3359, 5525, 3837, 3373, 5527,
3839, 3375, 5560, 4955, 3834, 7155, 6042, 5520, 6291, 4740, 6044, 5338, 4972, 4026,
6295, 6040, 4746, 3852, 7167, 5526, 3851, 7169, 5528, 3891, 7157, 4022, 5623, 5275,
6191, 3538, 3333, 5339, 4956, 3853, 7181, 5704, 5258, 4973, 5277, 4957, 3855, 3377,
5529, 3857, 3379, 5581, 3335, 3552, 5563, 3515, 3859, 3391, 5566, 3517, 5625, 5279,
4958, 3836, 7159, 4028, 3838, 9171, 4745, 6278, 4748, 5270, 4959, 4418, 5641, 4974,
4060, 6297, 4062, 5627, 5274, 4975, 8230, 4977, 3856, 3393, 5567, 3519, 3893, 3395,
5568, 3533, 5291, 4978, 3894, 7171, 4747, 3858, 3397, 5569, 4979, 3895, 3399, 5583,
3337, 3556, 3511, 5585, 3339, 3558, 3531, 5351, 4992, 5266, 4993, 5823, 3897, 7022,
5629, 5278, 6195, 5350, 4994, 5268, 4995, 5280, 4997, 3892, 7041, 5564, 5293, 6299,
4042, 5606, 7173, 4749, 3896, 3551, 5589, 3711, 3572, 5723, 3899, 3553, 5645, 5356,
4996, 7026, 6025, 5284, 4990, 4066, 6027, 5286, 4999, 4080, 6415, 5580, 6197, 3578,
3535, 5295, 6199, 3592, 5741, 3574, 5353, 6311, 3594, 5297, 4452, 5647, 5290, 6315,
3596, 3555, 5649, 5358, 6314, 5370, 6316, 3712, 5288, 6317, 5374, 6331, 6318, 3714,
5294, 6335, 6334, 5378, 6319, 5390, 6336, 3716, 7040, 4782, 5600, 6338, 6370, 4780,
6290, 4786, 6046, 7306, 4783, 5661, 5530, 6417, 5584, 5299, 4450, 6048, 3718, 5296,
6350, 4784, 5608, 6372, 4788, 6292, 4900, 4064, 5633, 6451, 4902, 5620, 6455, 6062,
5586, 6419, 5588, 3715, 5394, 6337, 8312, 5725, 5611, 5355, 6339, 3734, 5357, 8117,
3537, 5613, 5359, 6351, 3736, 3557, 5727, 5615, 5371, 6355, 3738, 3539, 5373, 6357,
3752, 5663, 5533, 6457, 4068, 5617, 5630, 6359, 4904, 5631, 6371, 4906, 4456, 6029,
5624, 5634, 6352, 4908, 5614, 5375, 6356, 3756, 7042, 5706, 3559, 5729, 5616, 7175,
6141, 3758, 3571, 5377, 8119, 3573, 5619, 5379, 6358, 3772, 5700, 6374, 4920, 4458,
5667, 5534, 6459, 4044, 5636, 6375, 6304, 5396, 6377, 4924, 5635, 6379, 4926, 7251,
4785, 5618, 5536, 6391, 4922, 4082, 5669, 4470, 6060, 6712, 5640, 6378, 4928, 4472,
6225, 6294, 4940, 4084, 5637, 4474, 6227, 4478, 5681, 5391, 6390, 4942, 5626, 7253,
4789, 5638, 5538, 6395, 6306, 4944, 5628, 6471, 4946, 4490, 6229, 4046, 7046, 4948,
5660, 6475, 6064, 5550, 6477, 5664, 5535, 6479, 5708, 3575, 5393, 6397, 3778, 3577,
5395, 6399, 3792, 5745, 3774, 5397, 8131, 3579, 5639, 5399, 6392, 5746, 3794, 5740,
6394, 5556, 6491, 5720, 6412, 5724, 5670, 6396, 6716, 7048, 5726, 7252, 4923, 5671,
5531, 6711, 3796, 3591, 5747, 3912, 5781, 3717, 3914, 5537, 8133, 3593, 5811, 3595,
5749, 3916, 3597, 5783, 3719, 3918, 3599, 5539, 6495, 5748, 3934, 5551, 6715, 3936,
3713, 5683, 5731, 6714, 5558, 6717, 5570, 6719, 3938, 3731, 5553, 6731, 3952, 5728,
5673, 5555, 6497, 5780, 6499, 5786, 3751, 5744, 5574, 6735, 6296, 4960, 4086, 7045,
5644, 5578, 6611, 5590, 6737, 3956, 3753, 5685, 5730, 6718, 3972, 5784, 6631, 6730,
6414, 5788, 6416, 7308, 4925, 5666, 6755, 6066, 3958, 5668, 5573, 6635, 6450, 4962,
5680, 6637, 4492, 6245, 6068, 3974, 5674, 6639, 4494, 6080, 4964, 5678, 6671, 6734,
6452, 4966, 7028, 5689, 5675, 6630, 6736, 6418, 5900, 4496, 6247, 4088, 5677, 4630,
6675, 6084, 6738, 6470, 4968, 4612, 5825, 6456, 6308, 5904, 4634, 6677, 4200, 6615,
5594, 6739, 6458, 5906, 7177, 4927, 5679, 5557, 8137, 3733, 5691, 5559, 6617, 5596,
6751, 5908, 3735, 5571, 6757, 3978, 3737, 5575, 6759, 3992, 5785, 3739, 3994, 5577,
8139, 3755, 5646, 7352, 4929, 5684, 5695, 6750, 6342, 5920, 4614, 5693, 6771, 6344,
5734, 6472, 6340, 6752, 5648, 5736, 6474, 6346, 6756, 6082, 5924, 4636, 6679, 4040,
6478, 5926, 4670, 6249, 4616, 7047, 8302, 5789, 5690, 6758, 6348, 5738, 6490, 6360,
6702, 5686, 6770, 6086, 3996, 7060, 4945, 5688, 5735, 6492, 6362, 5928, 5694, 5579,
6619, 5696, 6772, 6364, 5750, 6494, 5940, 4618, 5697, 4830, 6691, 5946, 4672, 5827,
4674, 5829, 4678, 5800, 6774, 6088, 6778, 5770, 6775, 6790, 6792, 5948, 5314, 5591,
6777, 5316, 3757, 5804, 7179, 4048, 5814, 7191, 4947, 5806, 3759, 5808, 3771, 5941,
8314, 5593, 6811, 7312, 5923, 5699, 5595, 6779, 5318, 3773, 5597, 8151, 3775, 5813,
3777, 5860, 6795, 5840, 6794, 5846, 6796, 7062, 4949, 5816, 3779, 5944, 5756, 6791,
5960, 8153, 5815, 7255, 6145, 5514, 5599, 6797, 5516, 3791, 5945, 5518, 3793, 5733,
6799, 5716, 3795, 5947, 5714, 5737, 8157, 3797, 5817, 3799, 5841, 6912, 5964, 5739,
6695, 5758, 6911, 5774, 6697, 8330, 6915, 5818, 3911, 5925, 8231, 6917, 5820, 6699,
4202, 6402, 5966, 3913, 5861, 3915, 5863, 3917, 5824, 6851, 6366, 7500, 6425, 5844,
6950, 4402, 5845, 6496, 6368, 5968, 5830, 6855, 6382, 7340, 6384, 5778, 6614, 5790,
6812, 7342, 7346, 7316, 7183, 5847, 7256, 4963, 5867, 7257, 8023, 5819, 7258, 6147,
5794, 6831, 6914, 5826, 6815, 7066, 4967, 5828, 6817, 7068, 4969, 5833, 6819, 7348,
6386, 7356, 6388, 9300, 6380, 6916, 7080, 6125, 5834, 6951, 8304, 5753, 6835, 7318,
5927, 5831, 6919, 5880, 6857, 7362, 5929, 5835, 3919, 7185, 3931, 5718, 3933, 5751,
6931, 5796, 3951, 5961, 3935, 5837, 3953, 5869, 3955, 5864, 7193, 6427, 5866, 3957,
5868, 3973, 5881, 6955, 5884, 7195, 6406, 7366, 7189, 5848, 9270, 6127, 4638, 5839,
4690, 6200, 6704, 5836, 6918, 5886, 6859, 4404, 5849, 6952, 5888, 3971, 7360, 6935,
5838, 3975, 5883, 6957, 4406, 7049, 4408, 5885, 6956, 8306, 7523, 5889, 3959, 7082,
5949, 5914, 5755, 6937, 5916, 3977, 5963, 3937, 5851, 3979, 7081, 3939, 5918, 3991,
5757, 8159, 3993, 5853, 3995, 5967, 3997, 5855, 3999, 7380, 6149, 5930, 8171, 5113,
5857, 4692, 7063, 6129, 5850, 6612, 7368, 6167, 5856, 6891, 7382, 5969, 5858, 6895,
7386, 6161, 7502, 6429, 7086, 6169, 7506, 6445, 7388, 5111, 5934, 4694, 6261, 6706,
7088, 6181, 5936, 4696, 6267, 4422, 7067, 4424, 7069, 4426, 7083, 6185, 5890, 6958,
4428, 9023, 6269, 4812, 7085, 6189, 5938, 5894, 6959, 4482, 7089, 5956, 7358, 9123,
5859, 4814, 7200, 6341, 5950, 4816, 7223, 6447, 7202, 6345, 5958, 5115, 5759, 6934,
5970, 8173, 5117, 5891, 6971, 7508, 5119, 5771, 6930, 8316, 7113, 7423, 7425, 7402,
7341, 5974, 5773, 6837, 7370, 6347, 5978, 5311, 5775, 6616, 7372, 6349, 5990, 8177,
5513, 5893, 6897, 4462, 7427, 7406, 7345, 7562, 7525, 5895, 7111, 7347, 5994, 5777,
8179, 5515, 5897, 7115, 7349, 5996, 7117, 7361, 5517, 5899, 6899, 6408, 9302, 7363,
6939, 5896, 6975, 7566, 7119, 7408, 9002, 7367, 8193, 7225, 6404, 7520, 6449, 7206,
6361, 7522, 6461, 7526, 6467, 7208, 6469, 7220, 6442, 7528, 6481, 7700, 6444, 7560,
6485, 7240, 6708, 9000, 6367, 8512, 7227, 4464, 7229, 4442, 7242, 6722, 7246, 6724,
7248, 6726, 7260, 6725, 7230, 6936, 7270, 6369, 7512, 7441, 7568, 5519, 7231, 6938,
9312, 7369, 6972, 7266, 6977, 7226, 8411, 7527, 7411, 7381, 5315, 7330, 6974, 7228,
6839, 7272, 6381, 7336, 6978, 9004, 5779, 6618, 9330, 6970, 4818, 9271, 6385, 6990,
8300, 6727, 7236, 6979, 7280, 6991, 7338, 5313, 5791, 6992, 7582, 7385, 7378, 9304,
5793, 6995, 7392, 7383, 5317, 7390, 6389, 7396, 7516, 7389, 7702, 7442, 7586, 7197,
7422, 7429, 7426, 7445, 7588, 5319, 7530, 6997, 7518, 5511, 5795, 6816, 7552, 7447,
7428, 9027, 7233, 6999, 7222, 6489, 7706, 6446, 7580, 6625, 7238, 6994, 7262, 6627,
7268, 6629, 7278, 6604, 7536, 8191, 7529, 6641, 7538, 8197, 5797, 8413, 7563, 7413,
7449, 7446, 7448, 9308, 5799, 6830, 6996, 7708, 6645, 7550, 6729, 7282, 6741, 7556,
6745, 7286, 6728, 9008, 5931, 8199, 6285, 6448, 9340, 6700, 6634, 7558, 6647, 7288,
6649, 7290, 6462, 7722, 7461, 7567, 7415, 7463, 7569, 7417, 7462, 7583, 7419, 7482,
7466, 7726, 7467, 7585, 7451, 7728, 9041, 7570, 8311, 5713, 7235, 8313, 5715, 7237,
8317, 5717, 7239, 41131, 8318, 5719, 7259, 6742, 7740, 6744, 7572, 6747, 7292, 6749,
7412, 7561, 5913, 7271, 6781, 7712, 7742, 7746, 7578, 9125, 7273, 8319, 5915, 7275,
6785, 7716, 7592, 7581, 5711, 7590, 6789, 7416, 7748, 9342, 7720, 6636, 7596, 6825,
7468, 9127, 7261, 8513, 7245, 6464, 7780, 6466, 7782, 6468, 9500, 6281, 8334, 7730,
6638, 9334, 8331, 8514, 7247, 4466, 7249, 4444, 7400, 6746, 7296, 6748, 9042, 7786,
6672, 7788, 6674, 7736, 6678, 9344, 8336, 8516, 7263, 6667, 7420, 6661, 7738, 6692,
7900, 4468, 9029, 4204, 6670, 6720, 6690, 6740, 6482, 7902, 4484, 7241, 6782, 7440,
6784, 7450, 6786, 7418, 9348, 9338, 8333, 8533, 8233, 8237, 4834, 7277, 4604, 7279,
4606, 7291, 6788, 9044, 7750, 6694, 7752, 6484, 7906, 4486, 7267, 4488, 9045, 6204,
8338, 8517, 7269, 6685, 7452, 6902, 7460, 6669, 7456, 6486, 7908, 4602, 7281, 6904,
7458, 6681, 7756, 6488, 9360, 6780, 6696, 6900, 4608, 9047, 4206, 8251, 6906, 7470,
6689, 7472, 6606, 7758, 6602, 7920, 4622, 7283, 6827, 7478, 6829, 7490, 6802, 7922,
7469, 7483, 7481, 7926, 7486, 7485, 7488, 9362, 7928, 4836, 7293, 6841, 7718, 9048,
9364, 8530, 8239, 4838, 6814, 7940, 4624, 7285, 6608, 9368, 6908, 4890, 6289, 4446,
7480, 6922, 7800, 6845, 7802, 6924, 7806, 6847, 7808, 6849, 7820, 6642, 7942, 4626,
7289, 4448, 9040, 6920, 4850, 6861, 7946, 4628, 9049, 4208, 6818, 9370, 6925, 8234,
8537, 8253, 6867, 7492, 6869, 7496, 7489, 7725, 7812, 7589, 7727, 7816, 7199, 7723,
7453, 7729, 7455, 7741, 7772, 7745, 7778, 5911, 5933, 8257, 8027, 7295, 6881, 7792,
7842, 7948, 9022, 7823, 8417, 7783, 6885, 7770, 6944, 7790, 6889, 7796, 7846, 7962,
7785, 7457, 7966, 7459, 7825, 7471, 7747, 7818, 9111, 7749, 6834, 7950, 8123, 7297,
4802, 7827, 7822, 7829, 7826, 7841, 7968, 9024, 7299, 4852, 7845, 9382, 7781, 7912,
9384, 5935, 8236, 8519, 7847, 7852, 7789, 7848, 9314, 7923, 8419, 7849, 6644, 7960,
8127, 7473, 7861, 7513, 7863, 7475, 7866, 7515, 7867, 7517, 7869, 7477, 7868, 9113,
7881, 8351, 9502, 7883, 7311, 9388, 5917, 7830, 8353, 7925, 7479, 7927, 7491, 7929,
7493, 7885, 7315, 9504, 5937, 4856, 7495, 7862, 7945, 7882, 7941, 9508, 5919, 5939.
/Lars B
__________
Beautiful, Lars, well
done!
Best,
É.
__________
More Sweet
Suites
here.