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A290800
One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-6). These are the numbers congruent to 1 mod 7 (except for the initial 0).
10
0, 1, 22, 120, 120, 9724, 26531, 144180, 144180, 17438583, 259560225, 259560225, 259560225, 83307283431, 180196293838, 2893088585234, 17135773115063, 116834564823866, 582095592798280, 10352577180260974, 55948157921753546, 454909489409813551
OFFSET
0,3
COMMENTS
x = ...140231,
x^2 = ...666661 = -6.
LINKS
Wikipedia, Hensel's Lemma.
FORMULA
a(0) = 0 and a(1) = 1, a(n) = a(n-1) + 3 * (a(n-1)^2 + 6) mod 7^n for n > 1.
EXAMPLE
a(1) = 1_7 = 1,
a(2) = 31_7 = 22,
a(3) = 231_7 = 120,
a(4) = 231_7 = 120,
a(5) = 40231_7 = 9724.
MAPLE
with(padic):
R:= [rootp(x^2+6, 7, 100)]:
R1:= op(select(t -> ratvaluep(evalp(t, 7, 1))=1, R)):
seq(ratvaluep(evalp(R1, 7, n)), n=0..100); # Robert Israel, Aug 11 2017
PROG
(PARI) a(n) = if (n, truncate(sqrt(-6+O(7^(n)))), 0)
CROSSREFS
Sequence in context: A100930 A260810 A274610 * A251930 A039612 A085828
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 10 2017
STATUS
approved