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

Neil Sloane njasloane at gmail.com
Fri Jun 13 06:30:36 CEST 2014

```Both Eric's sequence A243700 and Max's A243864 have
very striking graphs! (I'm glad Max provided so many terms, now we
can really see what is going on. When the sequence is mysterious,
we need a LOT of terms.)

The graphs suggest that one should be able to find at least a probabilistic
model for this problem.

Neil

On Fri, Jun 13, 2014 at 12:12 AM, Max Alekseyev <maxale at gmail.com> wrote:

> Such numbers are now listed in A243864.
>
> Regards,
> Max
>
>
> On Wed, Jun 11, 2014 at 9:48 PM, Robert G. Wilson v <rgwv at rgwv.com> wrote:
> > What a great sequence. I am glad that Éric did not wait until the end of
> year contest. Also at least for the terms presented, the following numbers
> have not yet appeared: 4, 6, 10, 12, 17, 19, 21, 23, ..., . I am also
> awaiting for the Mmca coding. Bob.
> >
> > -----Original Message-----
> > From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil
> Sloane
> > Sent: Wednesday, June 11, 2014 4:43 PM
> > To: Sequence Fanatics Discussion list
> > Subject: [seqfan] Re: a(n) divides the sum of the first a(n) terms of T.
> >
> > 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.
> > Email: njasloane at gmail.com
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> > _______________________________________________
> >
> > 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.