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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).
10
0, 6, 27, 223, 2281, 7083, 91118, 679363, 5620621, 22915024, 22915024, 1717766518, 13581726976, 13581726976, 498026779011, 1854472924709, 16097157454538, 115795949163341, 1046318005112169, 1046318005112169, 23844108375858455, 103636374673470456
OFFSET
0,2
COMMENTS
x = ...526436,
x^2 = ...666661 = -6.
LINKS
Wikipedia, Hensel's Lemma.
FORMULA
a(0) = 0 and a(1) = 6, a(n) = a(n-1) + 4 * (a(n-1)^2 + 6) mod 7^n for n > 1.
If n > 0, a(n) = 7^n - A290800(n).
EXAMPLE
a(1) = 6_7 = 6,
a(2) = 36_7 = 27,
a(3) = 436_7 = 223,
a(4) = 6436_7 = 2281,
a(5) = 26436_7 = 7083.
PROG
(PARI) a(n) = if (n, 7^n - truncate(sqrt(-6+O(7^(n)))), 0)
CROSSREFS
Sequence in context: A267630 A351737 A047778 * A360754 A367886 A351735
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 11 2017
STATUS
approved