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).

0, 6, 27, 223, 2281, 7083, 91118, 679363, 5620621, 22915024, 22915024, 1717766518, 13581726976, 13581726976, 498026779011, 1854472924709, 16097157454538, 115795949163341, 1046318005112169, 1046318005112169, 23844108375858455, 103636374673470456

Offset: 0

Author

Seiichi Manyama, Aug 11 2017

Keywords

• nonn

Comments

x = ...526436,

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

Examples

			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.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1183
• Wikipedia, Hensel's Lemma.

Crossrefs

Cf. A290795, A290800.

Programs

PARI

a(n) = if (n, 7^n - truncate(sqrt(-6+O(7^(n)))), 0)

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).