

A290804


One of the two successive approximations up to 7^n for the 7adic 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
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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(n1) + 2 * (a(n1)^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



