login
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
OFFSET
0,2
COMMENTS
x = ...554044,
x^2 = ...666662 = -5.
LINKS
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
Sequence in context: A309906 A196247 A196250 * A068088 A118901 A373287
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 11 2017
STATUS
approved