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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). 10
0, 4, 32, 32, 1404, 13409, 97444, 215093, 3509265, 15038867, 257160509, 1669536754, 5624190240, 19465477441, 310132508662, 310132508662, 28795501568320, 228193084985926, 1623976168909168, 8137630560550964, 76531001672789822, 555284599458461828 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

x   = ...554044,

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

LINKS

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

Wikipedia, Hensel's Lemma.

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).

EXAMPLE

a(1) =    4_7 = 4,

a(2) =   44_7 = 32,

a(3) =   44_7 = 32,

a(4) = 4044_7 = 1404.

PROG

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

CROSSREFS

Cf. A290799, A290806.

Sequence in context: A309906 A196247 A196250 * A068088 A118901 A275713

Adjacent sequences:  A290806 A290807 A290808 * A290810 A290811 A290812

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 11 2017

STATUS

approved

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Last modified September 17 22:53 EDT 2019. Contains 327147 sequences. (Running on oeis4.)