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 A019445 Form a permutation of the positive integers, p_1, p_2, ..., such that the average of each initial segment is an integer, using the greedy algorithm to define p_n; sequence gives p_1 + ... + p_n. 3
 1, 4, 6, 12, 20, 24, 35, 40, 54, 70, 77, 96, 117, 126, 150, 160, 187, 216, 228, 260, 273, 308, 345, 360, 400, 442, 459, 504, 522, 570, 620, 640, 693, 748, 770, 828, 851, 912, 975, 1000, 1066, 1092, 1161, 1232, 1260, 1334, 1410, 1440, 1519, 1550 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It appears that a(n) is divisible by n. - Michael Somos, Jan 29 2004 Somos's conjecture is proved in both Shapovalov (1996) and Venkatachala (2009). - Jeffrey Shallit, Jul 18 2023 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 J. Shallit, Proving properties of some greedily-defined integer recurrences via automata theory, arXiv:2308.06544 [cs.DM], August 12 2023. A. Shapovalov, Problem M1517 (in Russian), Kvant 5 (1995), 20-21. English translation appeared in Quantum problem M185, Sept/October 1996 (beware, file is 75Mb). The Math Forum, Problem of the Week 818. B. J. Venkatachala, A curious bijection on natural numbers, JIS 12 (2009) 09.8.1. FORMULA Partial sums of A019444. - Sean A. Irvine, Mar 17 2019 a(n) = n * A019446(n). - Joerg Arndt, Jul 23 2023 CROSSREFS Cf. A019444, A019446. Sequence in context: A057339 A336552 A160856 * A119638 A178547 A168674 Adjacent sequences: A019442 A019443 A019444 * A019446 A019447 A019448 KEYWORD nonn AUTHOR R. K. Guy, Tom Halverson (halverson(AT)macalester.edu) STATUS approved

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Last modified February 25 00:32 EST 2024. Contains 370308 sequences. (Running on oeis4.)