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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

x   = ...526436,

x^2 = ...666661 = -6.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1183

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

Cf. A290795, A290800.

Sequence in context: A060977 A267630 A047778 * A322233 A164985 A048436

Adjacent sequences:  A290799 A290800 A290801 * A290803 A290804 A290805

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 11 2017

STATUS

approved

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Last modified April 10 02:39 EDT 2020. Contains 333392 sequences. (Running on oeis4.)