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A290806
One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-5). These are the numbers congruent to 3 mod 7 (except for the initial 0).
10
0, 3, 17, 311, 997, 3398, 20205, 608450, 2255536, 25314740, 25314740, 307789989, 8217096961, 77423532966, 368090564187, 4437429001281, 4437429001281, 4437429001281, 4437429001281, 3261264624822179, 3261264624822179, 3261264624822179, 1120352992791390193
OFFSET
0,2
COMMENTS
x = ...112623,
x^2 = ...666662 = -5.
LINKS
FORMULA
a(0) = 0 and a(1) = 3, a(n) = a(n-1) + (a(n-1)^2 + 5) mod 7^n for n > 1.
EXAMPLE
a(1) = 3_7 = 3,
a(2) = 23_7 = 17,
a(3) = 623_7 = 311,
a(4) = 2623_7 = 997.
MAPLE
with(padic):
R:= [rootp(x^2+5, 7, 100)]:
R1:= op(select(t -> ratvaluep(evalp(t, 7, 1))=3, R)):
seq(ratvaluep(evalp(R1, 7, n)), n=0..100); # Robert Israel, Aug 13 2017
PROG
(PARI) a(n) = if (n, truncate(sqrt(-5+O(7^(n)))), 0)
CROSSREFS
Sequence in context: A155201 A062622 A271609 * A009592 A051294 A192556
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 11 2017
STATUS
approved