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A290802
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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).
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10
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0, 6, 27, 223, 2281, 7083, 91118, 679363, 5620621, 22915024, 22915024, 1717766518, 13581726976, 13581726976, 498026779011, 1854472924709, 16097157454538, 115795949163341, 1046318005112169, 1046318005112169, 23844108375858455, 103636374673470456
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OFFSET
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0,2
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COMMENTS
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x = ...526436,
x^2 = ...666661 = -6.
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LINKS
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FORMULA
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a(0) = 0 and a(1) = 6, a(n) = a(n-1) + 4 * (a(n-1)^2 + 6) mod 7^n for n > 1.
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EXAMPLE
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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.
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PROG
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(PARI) a(n) = if (n, 7^n - truncate(sqrt(-6+O(7^(n)))), 0)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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