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A290804 One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-3). These are the numbers congruent to 5 mod 7 (except for the initial 0). 10
0, 5, 12, 306, 306, 2707, 69935, 658180, 4775895, 10540696, 10540696, 575491194, 4530144680, 59895293484, 544340345519, 1900786491217, 20891032530989, 87356893670191, 319987407657398, 10090468995120092, 44287154551239521, 203871687146463523 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

x   = ...410615,

x^2 = ...666664 = -3.

LINKS

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

Wikipedia, Hensel's Lemma.

FORMULA

a(0) = 0 and a(1) = 5, a(n) = a(n-1) + 2 * (a(n-1)^2 + 3) mod 7^n for n > 1.

If n > 0, a(n) = 7^n - A290803(n).

EXAMPLE

a(1) =     5_7 = 5,

a(2) =    15_7 = 12,

a(3) =   615_7 = 306,

a(4) =   615_7 = 306,

a(5) = 10615_7 = 2707.

PROG

(PARI) a(n) = if (n, 7^n - truncate(sqrt(-3+O(7^(n)))), 0)

CROSSREFS

Cf. A290797, A290803.

Sequence in context: A195538 A330218 A047658 * A146542 A264873 A116058

Adjacent sequences:  A290801 A290802 A290803 * A290805 A290806 A290807

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 11 2017

STATUS

approved

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Last modified December 14 14:50 EST 2019. Contains 329979 sequences. (Running on oeis4.)