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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). 10

%I

%S 0,4,32,32,1404,13409,97444,215093,3509265,15038867,257160509,

%T 1669536754,5624190240,19465477441,310132508662,310132508662,

%U 28795501568320,228193084985926,1623976168909168,8137630560550964,76531001672789822,555284599458461828

%N 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 x = ...554044,

%C x^2 = ...666662 = -5.

%H Seiichi Manyama, <a href="/A290809/b290809.txt">Table of n, a(n) for n = 0..1183</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hensel%27s_lemma">Hensel's Lemma</a>.

%F 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 If n > 0, a(n) = 7^n - A290806(n).

%e a(1) = 4_7 = 4,

%e a(2) = 44_7 = 32,

%e a(3) = 44_7 = 32,

%e a(4) = 4044_7 = 1404.

%o (PARI) a(n) = if (n, 7^n - truncate(sqrt(-5+O(7^(n)))), 0)

%Y Cf. A290799, A290806.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 11 2017

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Last modified October 15 17:24 EDT 2019. Contains 328037 sequences. (Running on oeis4.)