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A290809 One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-5). These are the numbers congruent to 4 mod 7 (except for the initial 0).

%I A290809 #19 Aug 14 2017 09:37:52
%S A290809 0,4,32,32,1404,13409,97444,215093,3509265,15038867,257160509,
%T A290809 1669536754,5624190240,19465477441,310132508662,310132508662,
%U A290809 28795501568320,228193084985926,1623976168909168,8137630560550964,76531001672789822,555284599458461828
%N A290809 One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-5). These are the numbers congruent to 4 mod 7 (except for the initial 0).
%C A290809 x   = ...554044,
%C A290809 x^2 = ...666662 = -5.
%H A290809 Seiichi Manyama, <a href="/A290809/b290809.txt">Table of n, a(n) for n = 0..1183</a>
%H A290809 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hensel%27s_lemma">Hensel's Lemma</a>.
%F A290809 a(0) = 0 and a(1) = 4, a(n) = a(n-1) + 6 * (a(n-1)^2 + 5) mod 7^n for n > 1.
%F A290809 If n > 0, a(n) = 7^n - A290806(n).
%e A290809 a(1) =    4_7 = 4,
%e A290809 a(2) =   44_7 = 32,
%e A290809 a(3) =   44_7 = 32,
%e A290809 a(4) = 4044_7 = 1404.
%o A290809 (PARI) a(n) = if (n, 7^n - truncate(sqrt(-5+O(7^(n)))), 0)
%Y A290809 Cf. A290799, A290806.
%K A290809 nonn
%O A290809 0,2
%A A290809 _Seiichi Manyama_, Aug 11 2017