# [seqfan] Re: a(n) divides the sum of the first a(n) terms of T.

Neil Sloane njasloane at gmail.com
Wed Jun 11 22:43:21 CEST 2014

```Alexander's proposed definition doesn't do this justice. I prefer Eric's
description, but slightly modified.

The lexicographically earliest sequence of distinct terms
with a(1) = 1 such that
a(n) divides the sum of the first a(n) terms. ?

It is a lovely sequence. Eric, will you submit it?

Neil

On Wed, Jun 11, 2014 at 11:35 AM, <apovolot at gmail.com> wrote:

> Should this sequence be named as:
> "The self referenced sequence, with such terms a(n) that
> Mod (Sum (a(j), j=1...a(n)),a(n) ) = 0
>
> Alexander R. Povolotsky
>
> > On Jun 11, 2014, at 7:08 AM, Eric Angelini <Eric.Angelini at kntv.be>
> wrote:
> >
> >
> > Hello SeqFans,
> >
> > Jean-Marc Falcoz has computed the T seq such that:
> >
> > a(n) divides the sum of the first a(n) terms of T.
> >
> > This is:
> >
> > 1 divides the sum of the first 1 term  (yes:  1/1=1)
> > 3 divides the sum of the first 3 terms (yes:  6/3=2)
> > 2 divides the sum of the first 2 terms (yes:  4/2=2)
> > 5 divides the sum of the first 5 terms (yes: 20/5=4)
> > 9 divides the sum of the first 9 terms (yes: 63/9=7)
> > 7 divides the sum of the first 7 terms (yes: 35/7=5)
> > 8 divides the sum of the first 8 terms (yes: 48/8=6)
> > ...
> > The first column above is the seq T.
> > Many thanks, Jean-Marc!
> > Best,
> > É.
> >
> > {1, 3, 2, 5, 9, 7, 8, 13, 15, 11, 14, 16, 26, 24, 41, 29, 18, 28, 20, \
> > 30, 22, 32, 25, 33, 43, 45, 31, 37, 50, 52, 54, 56, 58, 35, 87, 38, \
> > 55, 67, 40, 60, 72, 44, 63, 77, 79, 47, 70, 49, 121, 88, 53, 129, 94, \
> > 96, 98, 100, 59, 89, 105, 107, 62, 158, 113, 65, 102, 68, 103, 189, \
> > 71, 109, 127, 201, 74, 118, 76, 120, 138, 80, 123, 143, 82, 128, 84, \
> > 130, 86, 132, 154, 156, 247, 91, 142, 93, 144, 167, 97, 147, 172, \
> > 174, 101, 153, 179, 181, 183, 106, 161, 188, 190, 110, 276, 196, 112, \
> > 286, 202, 115, 180, 117, 182, 210, 122, 184, 215, 217, 219, 125, 194, \
> > 131, 192, 227, 229, 231, 233, 235, 134, 208, 136, 346, 139, 213, 386, \
> > 141, 220, 253, 255, 257, 146, 228, 262, 149, 232, 151, 234, 155, 387, \
> > 274, 431, 279, 159, 405, 285, 162, 414, 291, 164, 260, 166, 428, 300, \
> > 169, 268, 171, 270, 308, 175, 273, 313, 177, 278, 185, 453, 322, 324, \
> > 326, 328, 330, 332, 187, 296, 337, 339, 341, 193, 303, 539, 349, 197, \
> > 311, 354, 199, 316, 203, 517, 363, 365, 205, 531, 207, 537, 375, 211, \
> > 335, 380, 214, 552, 600, 389, 218, 566, 395, 397, 399, 222, 360, 224, \
> > 362, 226, 364, 410, 412, 643, 236, 369, 420, 422, 424, 426, 664, 238, \
> > 388, 240, 390, 242, 392, 244, 394, 246, 396, 446, 249, 400, 251, 402, \
> > 254, 403, 457, 459, 258, 409, 464, 261, 413, 469, 471, 264, 684, 266, \
> > 690, 269, 427, 484, 486, 272, 434, 491, 493, 277, 439, 498, 500, 502, \
> > 281, 448, 283, 450, 287, 735, 514, 516, 289, 460, 292, 461, 524, 294, \
> > 466, 297, 467, 532, 299, 472, 837, 302, 478, 543, 305, 482, 307, 791, \
> > 860, 310, 492, 558, 314, 495, 563, 317, 499, 568, 319, 504, 321, 506, \
> > 576, 325, 509, 581, 583, 329, 515, 588, 590, 333, 521, 595, 336, 525, \
> > 936, 603, 340, 533, 608, 610, 343, 540, 345, 542, 618, 348, 546, 623, \
> > 351, 550, 353, 905, 632, 356, 914, 358, 562, 361, 923, 645, 647, 649, \
> > 651, 653, 367, 578, 370, 579, 661, 372, 584, 374, 586, 669, 377, 967, \
> > 379, 594, 678, 382, 598, 384, 984, 391, 599, 1077, 693, 695, 697, \
> > 699, 701, 398, 616, 706, 708, 710, 712, 714, 716, 404, 1034, 722, \
> > 724, 726, 407, 644, 411, 1053, 1145, 738, 740, 742, 744, 416, 662, \
> > 418, 1082, 421, 667, 756, 758, 425, 673, 763, 765, 767, 769, 430, \
> > 1114, 775, 433, 1123, 781, 436, 696, 438, 698, 789, 441, 702, 443, \
> > 704, 445, 1151, 801, 449, 711, 806, 808, 452, 718, 813, 455, 1177, \
> > 458, 725, 822, 824, 826, 828, 463, 736, 833, 468, 1204, 839, 841, \
> > 843, 473, 748, 848, 850, 475, 1231, 477, 760, 859, 480, 764, 483, \
> > 1247, 868, 870, 487, 773, 875, 489, 778, 494, 777, 883, 885, 887, \
> > 889, 497, 790, 894, 896, 898, 503, 797, 903, 1409, 507, 805, 911, \
> > 510, 809, 916, 512, 814, 518, 812, 924, 926, 928, 930, 520, 1346, \
> > 1457, 523, 834, 942, 944, 527, 840, 529, 842, 534, 1372, 956, 958, \
> > 960, 536, 854, 965, 541, 856, 970, 972, 974, 976, 545, 1413, 982, \
> > 548, 874, 551, 1425, 991, 993, 554, 884, 556, 886, 559, 1445, 1005, \
> > 561, 1455, 1011, 1013, 565, 902, 1018, 569, 1473, 1024, 571, 912, \
> > 573, 1487, 575, 918, 1036, 580, 920, 1041, 1043, 1045, 585, 1511, \
> > 1051, 1638, 1056, 589, 941, 1061, 1063, 592, 948, 596, 1542, 1072, \
> > 1074, 601, 955, 1079, 1081, 1083, 604, 1568, 1089, 606, 1578, 609, \
> > 975, 1098, 1100, 612, 1594, 614, 986, 617, 987, 1112, 1732, 620, 996, \
> > 622, 998, 1746, 625, 1004, 627, 1006, 629, 1008, 631, 1010, 1138, \
> > 634, 1014, 636, 1016, 638, 1656, 640, 1022, 642, 1666, 1157, 1159, \
> > 1161, 648, 1033, 1166, 1168, 652, 1039, 1173, 1175, 655, 1046, 657, \
> > 1048, 659, 1050, 663, 1711, 1190, 1192, 1194, 666, 1062, 1199, 670, \
> > 1065, 1874, 672, 1744, 1211, 675, 1078, 677, 1080, 1219, 680, 1084, \
> > 682, 1086, 685, 1087, 1230, 687, 1092, 689, 1094, 1238, 692, 1790, \
> > 1244, 700, 1099, 1249, 1251, 1253, 1255, 1257, 1259, 1261, 705, 1119, \
> > 1266, 1268, 709, 1125, 1273, 1275, 1277, 1279, 715, 1135, 1284, 1286, \
> > 719, 1141, 1291, 721, 1146, 1296, 727, 1147, 1301, 1303, 1305, 729, \
> > 1158, 731, 1160, 733, 1162, 737, 1897, 1320, 1322, 1324, 741, 1913, \
> > 1330, 1332, 745, 1181, 1337, 747, 1186, 1342, 750, 1940, 752, 1946, \
> > 754, 1198, 757, 1955, 1359, 1361, 761, 1207, 1366, 766, 1209, 1371, \
> > 1373, 1375, 1377, 770, 1221, 1382, 772, 1226, 1387, 776, 1229, 1392, \
> > 1394, 1396, 780, 2018, 1402, 783, 2027, 785, 1248, 787, 1250, 792, \
> > 2038, 1418, 1420, 1422, 794, 1262, 796, 1264, 1430, 799, 2067, 802, \
> > 1271, 1439, 804, 1276, 1444, 1446, 810, 1280, 1451, 1453, 815, 1285, \
> > 1458, 1460, 1462, 817, 2113, 819, 1300, 821, 1302, 1474, 825, 2129, \
> > 1480, 1482, 829, 1313, 2316, 831, 2151, 835, 2155, 1498, 1500, 838, \
> > 1331, 1505, 1507, 1509, 2352, 1514, 1516, 845, 1348, 847, 1350, 1524, \
> > 851, 1353, 1529, 853, 1358, 1534, 857, 2217, 1540, 861, 2225, 1546, \
> > 1548, 863, 1376, 865, 1378, 867, 1380, 1559, 871, 1383, 1564, 873, \
> > 1388, 1569, 1571, 877, 2271, 879, 1398, 881, 1400, 888, 1397, 1586, \
> > 1588, 1590, 1592, 2482, 1597, 891, 2309, 893, 2315, 1607, 897, 1427, \
> > 1612, 1614, 900, 1434, 904, 2336, 1623, 1625, 1627, 907, 2353, 909, \
> > 1450, 913, 2361, 1640, 1642, 1644, 917, 1461, 1649, 1651, 921, 1467, \
> > 2577, 925, 1472, 1662, 1664, 2592, 929, 1483, 1672, 1674, 932, 1490, \
> > 934, 1492, 937, 1493, 1685, 939, 2437, 943, 2441, 1695, 1697, 1699, \
> > 946, 1512, 949, 1513, 1707, 951, 1518, 953, 1520, 957, 2475, 1719, \
> > 1721, 1723, 961, 1531, 1728, 963, 1536, 966, 1537, 1736, 1738, 969, \
> > 1544, 1743, 973, 1547, 1748, 1750, 1752, 1754, 978, 1558, 980, 1560, \
> > 983, 1561, 1765, 1767, 988, 1566, 1772, 1774, 990, 1574, 1779, 994, \
> > 1577, 1784, 997, 1581, 1789, 1791, 1000, 2588, 1002, 2594, 1007, \
> > 1593, 1804, 1806, 1808, 1810, 1012, 1604, 1815, 1817, 1819, 1821, \
> > 1017, 1615, 1826, 1828, 1020, 1622, 1023, 2645, 1837, 1839, 1026, \
> > 1632, 1028, 1634, 1030, 1636, 1032, 2670, 1854, 1856, 1037, 1645, \
> > 1861, 1040, 2688, 1867, 1869, 1044, 1657, 2918, 1877, 1879, 1049, \
> > 1667, 1884, 1886, 1888, 1054, 1675, 1893, 1057, 1679, 1898, 1059, \
> > 1684, 1064, 1683, 1906, 1908, 1910, 1912, 1067, 1696, 1069, 1698, \
> > 1071, 1700, 1923, 1075, 1703, 1928, 1085, 2777, 1934, 1936, 1938, \
> > 3021, 1943, 1945, 1947, 1949, 1951, 1953, 1090, 1733, 1958, 1093, \
> > 1737, 1963, 1965, 1096, 2840, 1101, 1745, 1974, 1976}
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

--
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.