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 A290804 One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-3). These are the numbers congruent to 5 mod 7 (except for the initial 0). 10
 0, 5, 12, 306, 306, 2707, 69935, 658180, 4775895, 10540696, 10540696, 575491194, 4530144680, 59895293484, 544340345519, 1900786491217, 20891032530989, 87356893670191, 319987407657398, 10090468995120092, 44287154551239521, 203871687146463523 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS x   = ...410615, x^2 = ...666664 = -3. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1183 Wikipedia, Hensel's Lemma. FORMULA a(0) = 0 and a(1) = 5, a(n) = a(n-1) + 2 * (a(n-1)^2 + 3) mod 7^n for n > 1. If n > 0, a(n) = 7^n - A290803(n). EXAMPLE a(1) =     5_7 = 5, a(2) =    15_7 = 12, a(3) =   615_7 = 306, a(4) =   615_7 = 306, a(5) = 10615_7 = 2707. PROG (PARI) a(n) = if (n, 7^n - truncate(sqrt(-3+O(7^(n)))), 0) CROSSREFS Cf. A290797, A290803. Sequence in context: A195538 A330218 A047658 * A146542 A264873 A116058 Adjacent sequences:  A290801 A290802 A290803 * A290805 A290806 A290807 KEYWORD nonn AUTHOR Seiichi Manyama, Aug 11 2017 STATUS approved

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Last modified December 14 14:50 EST 2019. Contains 329979 sequences. (Running on oeis4.)