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 A322559 One of the two successive approximations up to 17^n for 17-adic integer sqrt(2). This is the 6 (mod 17) case (except for n = 0). 5
 0, 6, 244, 4290, 43594, 461199, 6140627, 344066593, 6088808015, 54919110102, 292094863096, 30532003369831, 544610447984326, 6953455057511697, 56476345222041382, 1066743304578446956, 21103704665147157507, 118426088416480894469, 11699789754825195592947 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n > 0, a(n) is the unique solution to x^2 == 2 (mod 17^n) in the range [0, 17^n - 1] and congruent to 6 modulo 17. A322560 is the approximation (congruent to 11 mod 17) of another square root of 2 over the 17-adic field. LINKS Wikipedia, p-adic number FORMULA For n > 0, a(n) = 17^n - A322560(n). a(n) = Sum_{i=0..n-1} A322561(i)*17^i. a(n) = A286877(n)*A322564(n) mod 17^n = A286878(n)*A322563(n) mod 17^n. EXAMPLE 6^2 = 36 = 2*17 + 2; 244^2 = 59536 = 206*17^2 + 2; 4290^2 = 18404100 = 3746*17^3 + 2. PROG (PARI) a(n) = truncate(sqrt(2+O(17^n))) CROSSREFS Cf. A322561, A322562. Approximations of 17-adic square roots: A286877, A286878 (sqrt(-1)); this sequence, A322560 (sqrt(2)); A322563, A322564 (sqrt(-2)). Sequence in context: A231019 A254009 A072228 * A229631 A206307 A229475 Adjacent sequences:  A322556 A322557 A322558 * A322560 A322561 A322562 KEYWORD nonn AUTHOR Jianing Song, Aug 29 2019 STATUS approved

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Last modified August 15 02:47 EDT 2022. Contains 356122 sequences. (Running on oeis4.)