A290809 One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-5). These are the numbers congruent to 4 mod 7 (except for the initial 0).

0, 4, 32, 32, 1404, 13409, 97444, 215093, 3509265, 15038867, 257160509, 1669536754, 5624190240, 19465477441, 310132508662, 310132508662, 28795501568320, 228193084985926, 1623976168909168, 8137630560550964, 76531001672789822, 555284599458461828

Offset: 0

Author

Seiichi Manyama, Aug 11 2017

Keywords

• nonn

Comments

x = ...554044,

x^2 = ...666662 = -5.

Examples

			a(1) =    4_7 = 4,
a(2) =   44_7 = 32,
a(3) =   44_7 = 32,
a(4) = 4044_7 = 1404.
		

Links

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

Crossrefs

Cf. A290799, A290806.

Programs

PARI

a(n) = if (n, 7^n - truncate(sqrt(-5+O(7^(n)))), 0)

Formula

a(0) = 0 and a(1) = 4, a(n) = a(n-1) + 6 * (a(n-1)^2 + 5) mod 7^n for n > 1.

If n > 0, a(n) = 7^n - A290806(n).