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A290802 One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-6). These are the numbers congruent to 6 mod 7 (except for the initial 0).

%I A290802 #19 Aug 14 2017 09:37:50
%S A290802 0,6,27,223,2281,7083,91118,679363,5620621,22915024,22915024,
%T A290802 1717766518,13581726976,13581726976,498026779011,1854472924709,
%U A290802 16097157454538,115795949163341,1046318005112169,1046318005112169,23844108375858455,103636374673470456
%N A290802 One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-6). These are the numbers congruent to 6 mod 7 (except for the initial 0).
%C A290802 x   = ...526436,
%C A290802 x^2 = ...666661 = -6.
%H A290802 Seiichi Manyama, <a href="/A290802/b290802.txt">Table of n, a(n) for n = 0..1183</a>
%H A290802 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hensel%27s_lemma">Hensel's Lemma</a>.
%F A290802 a(0) = 0 and a(1) = 6, a(n) = a(n-1) + 4 * (a(n-1)^2 + 6) mod 7^n for n > 1.
%F A290802 If n > 0, a(n) = 7^n - A290800(n).
%e A290802 a(1) =     6_7 = 6,
%e A290802 a(2) =    36_7 = 27,
%e A290802 a(3) =   436_7 = 223,
%e A290802 a(4) =  6436_7 = 2281,
%e A290802 a(5) = 26436_7 = 7083.
%o A290802 (PARI) a(n) = if (n, 7^n - truncate(sqrt(-6+O(7^(n)))), 0)
%Y A290802 Cf. A290795, A290800.
%K A290802 nonn
%O A290802 0,2
%A A290802 _Seiichi Manyama_, Aug 11 2017